I'M standing on a street in London, and the sun has disappeared from the sky.

A solar eclipse has created a shadowy half-light that, at noon, feels somehow unsettling and unnatural. And yet, all around me, people go about their business without so much as a glace towards the heavens.

Last night I witnessed a different eclipse, one that was heavy with foreboding. I gazed at a disc of pure light and, bit by bit, it was extinguished as the gods gave a sign that life was out of balance. A circle of black moved slowly across the golden face of the sun, casting the human figures beneath it into an uncertain world as hubris rained down upon Creon, King of Thebes.

Set design plays an important role at the climax of Antigone, which will be the flagship stage production at this year's Edinburgh International Festival when it settles into the King's Theatre for a 14-day run. In part, the extended box-office draw is down to the fact that it's directed by Ivo van Hove, whose 1999 production of India Song has entered EIF legend. Mostly, though, it's because Antigone is played by Juliette Binoche, the French actress who won an Oscar for The English Patient and who remains one of the greatest cinema stars of her generation.

I caught the play, complete with its visually arresting solar blackout, at one of its London dates in March. And here I am, the morning after, ready to interview Binoche but finding myself in the midst of a real solar eclipse. Clouds cover the London skies, so it's not possible to experience this astronomical event in its full glory as enjoyed by the population further north. But still: a genuine eclipse following so close after a fictional one? Sophocles himself might think fate was showing its hand ...

At first, a branch of Café Rouge was suggested for our meeting. I'm glad when that's changed, as it doesn't seem authentic enough for an actress who is on a level with Catherine Deneuve and Jeanne Moreau. So I return to the Barbican and wait in The Red Room, the private members' bar at the top of the arts complex. I'm only there for five minutes, however, when I'm told it would be better to join Binoche in her dressing room.

In person, dressed in stylishly nondescript black jeans and jacket, Binoche seems smaller than her 5'6", but her charisma fills the room. I quickly cast an eye around for clues to her personality. A clear plastic bag containing loose herbal tea sits next to a china pot and various make-up cases are laid out in front of the mirrors, but there are no personal mementos or photographs that I can see. It's a professional space where Binoche can retreat several hours before each performance to prepare - physically, mentally, spiritually.

We settle ourselves with small talk. She has never been to Edinburgh, but it's not a completely blank canvas.

"When she was 11 years old, my sister went to Edinburgh to learn English," she explains. "A family took her over and she stayed for about four weeks. She could speak English fluently, and I was mesmerised by it."

Did she pick up a Scottish accent?

"That I didn't know because I didn't speak English at the time. I was younger than her. I remember looking at the photographs, as she visited a lot of things around, and so I'm looking forward to discovering what she first saw."

Antigone's extended run will allow Binoche to spend quality time in Scotland with her 15-year-old daughter Hana (whose father is actor Benoit Magimel; she also has a 21-year-old son, Raphael, from a previous relationship). That said, she won't be slacking professionally, as she has two matinees to deliver as well as those 14 evening performances, with only Mondays off.

For many in the audience, it will be a rare chance to see a world-class movie star up close. And Binoche is good in the production, bringing an innocent and almost otherworldly element to this tale of the daughter of cursed Oedipus and her attempt to bury her warrior brother Polynices despite the tyrannical decree of Creon to leave his body to rot outside the city walls.

Different audiences will arrive hoping to see different Juliette Binoches. The Oscar-winner who regularly crosses over to English-language movies such as Chocolat, The Unbearable Lightness Of Being and (for three short but key scenes) Godzilla. The French superstar dubbed simply "La Binoche" by her home country's press, who has been placed on a pedestal for roles opposite the likes of Daniel Auteuil, Mathieu Amalric and Jean Reno. The international actress who for decades has taken on challenging parts under the eyes of the world's most exacting film directors - Jean-Luc Godard, Michael Haneke, David Cronenberg, Abbas Kiarostami, Krzysztof Kieslowski and Bruno Dumont among them.

What they'll get, of course, is someone who nightly sheds her screen celebrity skin in favour of stagecraft. This isn't the first time Binoche has swapped cinema for theatre. As early as 1984 she was playing Nina in a Parisian production of Chekhov's The Seagull. Her London stage debut came at the Almeida in 1997 with Pirandello's Naked, and three years later she was on Broadway in Pinter's Betrayal. Indeed, she's no stranger to the Barbican, where she starred in a modern-day adaptation of Strindberg's Mademoiselle Julie in 2012.

Still, Antigone is a major commitment for her. The play premiered in Luxembourg in February, will cross Europe and, after Edinburgh, transfer to the US where it finishes at the Kennedy Center in Washington DC at the end of October. Add in rehearsals and the fact that she was the one who instigated the project when given carte blanche by its producers, and that's effectively a year out of her life. Is that a tougher decision than signing on for a movie?

"No, for me it's the same commitment," she says. "I choose the films I really want to do and I don't have plans for my career - I think life has them for me. Theatre is very important for me because it's where I changed. I received so much as a member of the audience. I remember at 14 years old seeing the Ubu Roi of Peter Brook in Paris, and I was so transported by it, so moved by it, it was so joyful. I felt at the end of the play, 'That's what I want to do'. The experience of theatre is amazing, because the actor is giving you the information directly - it doesn't go through a medium, it goes through his thoughts and his spirit and his own body."

Throughout our conversation, Binoche continually reaches for - and grasps - the right words in what is, we must remember, a foreign language. In all honesty, I'd struggle to express the profound thoughts she has about Antigone. She has clearly weighed up every syllable of Anne Carson's new translation of the Sophocles text, and I get the feeling that even now, only a couple of weeks into Antigone's long run through 2015, she's still discovering depths to the character on a daily basis.

She talks about how the play is "the history of humanity", how there's a "disequilibrium in our lives" because those in power - and that means women as well as men - need to "take their feminine side". I suggest that this particular production of Antigone - which subtly uses CCTV-like video footage as back projection and throws around politically charged words like "patriot", "traitor" and "fatherland" - is very relevant in post-indyref, pre-election 2015.

"That was why I insisted to go for Antigone and not Medea or Electra," she explains. "The fear of women is so big. There's a deep jealousy behind all this, which is that women can create, have babies. I think [politicians'] power and muscles, and showing strength, is because of that fear."

I tell her how, only a few weeks before we meet, The Sun mocked up Nicola Sturgeon in a tartan bikini with Miley Cyrus's body on a wrecking ball. She hasn't seen that image, but mentions instead a Spanish edition of Vanity Fair that printed a photo, supposedly of a naked 18-year-old Angela Merkel, that had been doing the rounds online. "It's a way of ridiculing women," she insists.

Still on the subject of the play's relevance to 2015, I ask if she believes that the way Antigone goes about burying her brother Polynices, acting through devotion to the gods but against the rules of her society, makes her, in Creon's eyes at least, a terrorist?

"It reminded me of the jihadists who killed the journalists in Charlie Hebdo as well as the one who killed the four people in the Jewish store," admits Binoche, who was in Poland, not Paris, on the day of the shootings. "The family did not want to bury them, the French did not want to bury them because they were frightened and did not want to take responsibility of it, so the Muslim community actually buried those corpses in the middle of the night because no-one wanted to take care of them.

"For me, in the play, the humiliation that Creon wants to give Polynices is beyond comprehension. Creon's character is related to his head, so he can divide the good and the bad. For Antigone, it's the heart; she can recognise what's good and bad too, but for her there's something stronger, which is showing by an action the respect for the human being that anybody is. She's not trying to kill anyone, so it's different from a jihadist or a suicide bomber. She is just trying to heal a family and a curse that has been hammering her family for generations."

Binoche had to consider the actions of female suicide bombers a few years ago when she played a war zone photographer in the film A Thousand Times Goodnight. Although the film gets a bit wishy-washy when dealing with Western complicity over events in Afghanistan, there's a moment right at the end, when Binoche's character discovers the age of the bomber in her latest assignment, that cuts through the liberal guilt and reveals genuine human anguish. And it all happens on Binoche's face, those warm brown eyes now crinkled at the edges and smudged underneath by the cares of the world.

Personally, I think Binoche is one of the best actors in the world when it comes to camera close-ups. As a magazine journalist investigating student prostitution in Elles, entire narratives about self-doubt and desire flicker silently across her face; as the sculptor incarcerated in an asylum in Camille Claudel 1915, she delivers a sustained portrait of inner torment. It was quite different to see her on stage in Antigone, creating a character that's just as emotionally intense but having to project that across an auditorium.

"Well, for me it's the same actually," she counters. "Maybe on stage you don't see all the details because it depends if you're close or far away, but it's happening the same way for me. For me it's the same actress."

At the age of 51 is she now more drawn, at this later stage of her career, to challenging roles that have some sort of social agenda behind them?

"No, because in The Unbearable Lightness Of Being [1988] I was playing Czechoslovakian during the Communist time; and in Les Amants Du Pont-Neuf [1991], it was about people living outside on the street; and Mauvais Sang [1986] was about Aids, which was not really spoken about at the time but was just about to explode. I've always been keen to be human, first of all. It's not even political, it's more about talking about people, their lives, their being."

At the risk of being self-indulgent, I throw the names of a few film directors at her and ask if she'll say something about their working relationships.

Michael Haneke, with whom she made Code Unknown and Hidden: "I especially enjoyed Code Unknown because it was like he was scanning me. He knew exactly what was happening inside. And I liked that he was demanding, that he was always pushing. On Hidden I had a good time with him as well but he was more focused on Daniel Auteuil's character, which was more himself in the film. So for me there was more distance, but that was fine."

Krzysztof Kieslowski, director of Three Colours Blue: "Krzysztof was very easy to work with. We worked very quickly; he knew where to put the camera. The little tension we had sometimes was that he would make me rehearse, like, five times and do just one take. But it cannot be like the rehearsals because I'm not a puppet. You have to let the actor go as many times as he wants because he knows what he has inside; he knows that he can go further. When there was a technical problem Krzysztof would always do a second take. And I found it very unfair. So I asked him to consider me as a machine that had technical problems in order to do a second take."

Anthony Minghella, whom she worked with on The English Patient and Breaking And Entering: "The first one, especially, was like telepathy. He would think something and I would think what he was thinking, so we didn't need words that much because we were on the same tune. He was a writer before a director, and you really felt he had an ability of adapting to whatever situation we had to go through."

The English Patient was one of several films on which Binoche had to act in English, as she's currently having to do week in, week out with Antigone. Does working in a foreign language become one of the early building blocks for a character?

"No," she says, "because the words are a consequence of something deeper. The language is a tool, a medium, but it's not a purpose ... And I'm probably more at ease with the emotion than with the words."

Interview over, I leave the dressing room and pass backstage where I see, from the other side of the auditorium, the device that powers Antigone's theatrical eclipse. In an instant, all that magic and mystery is reduced to cogs and wheels. But I think back to what Binoche has just said, and realise what it is about her that has impressed me so much over the years. On screen, on stage, in English, in close-up, in conversation today - it's the unadorned emotion at the root of the scene that feeds her, and stage mechanics or spoken words are just the surface means of getting there.

Back out on the streets of London, the solar eclipse has all but passed ...

Antigone is at the King's Theatre, Edinburgh, from August 7-22 as part of the Edinburgh International Festival, www.eif.co.uk. A special performance recorded at the Barbican screens as part of BBC Four's Greek season tonight at 8pm