There's something quite charming about a successful actor cold-calling for a job.

Juliette Binoche is an Oscar winner, one of the few French actresses to regularly work in Hollywood and one of those even rarer creatures referenced with a definite article by her countrymen: La Binoche. And yet if there's a director she admires, she's never too proud to ask.

"I've always been very independent. And I've always said to the people I want to work with, 'Hey, I love what you're doing and maybe there'll be some kind of connection between us.' It's like love. If you're always waiting for things to happen, it's kind of boring."

She lets rip with her trademark peel of laughter, a spontaneous eruption that seems to lift the furniture of the Parisian hotel suite in which we're sitting. I realise that in her breezy enthusiasm Binoche has forgotten to take off her elegant coat and scarf; she remains seemingly unaware, and delightfully unencumbered.

The latest director to benefit from her forwardness is Bruno Dumont, a resolutely independent director whose films - from L'Humanité, to Outside Satan - are unadorned, downbeat dramas, often controversial, sometimes brilliant. They're also marked by his preference for non-professional actors, making Binoche's overture - she left him a phone message, inviting him to "call me back if you feel like it" - even more bold.

"His films stay with you for ever," she says, "I've always been very touched by them. Sometimes they're awkward, but that's okay, he's a real filmmaker. Nowadays, so many people think they're directors, but they don't have a sense of cinematography. Bruno has so much. I'd rather take less money, and make cinema."

Dumont did bite and the result, conceived specifically for Binoche, is Camille Claudel 1915. The film follows three days in the life of the tragic sculptress, long after she has fallen out with her mentor and lover Rodin, and a short while into her 29-year incarceration in an asylum, where she was erroneously committed by her family.

True to his modus operandi, Dumont surrounded his star with real psychiatric patients, employing their nurses to portray the sisters who presided over the asylum. Binoche was referred to throughout the shoot as Camille, so as not to confuse them. It's an austere and intensely moving film, anchored by Binoche's riveting portrait of loneliness and psychological torture.

"It was a question of how naked I could be in front of the camera, because Camille was totally bare, totally abandoned, totally forgotten. In the beginning it was quite painful, actually, I felt haunted by her spirit, almost frightened. And then there was a turning point in the middle of the shoot when I felt an acceptance, in myself, a joy to go on set and plunge into her, and then come out the other side."

Aside from the emotional challenge, there were technical ones, not least working alongside the patients, with no script. "I had vague directions - you're on a bench, waiting, or you're going outside for a walk. Beyond that I just had to be in the moment, to improvise."

She believes that whatever the level of mental handicap, there is within everyone "a sense of play", and it was this that galvanised her unusual co-stars. Yet she still had to carefully gauge how far to go with them, not least a young woman named Alexandra, in a key scene in which Camille forcibly rebuffs her.

"I instinctively wanted to protect Alex. But there were several takes that were not as strong as they could be. I was responsible for the scene. So there came a moment when I had to believe she was strong enough to take it - like with a child, there's the potential of an adult within them. So for the last take, which is in the movie, I just went for it, no bulls***. It's true that I surprised her, she felt betrayed, felt that I was really angry with her. Then she left. I followed her, and embraced her; she cried, I cried. Then 10 minutes later she was fine."

The late Anthony Minghella, who directed Binoche's Oscar-winning performance in The English Patient, once said, "She has no skin, so tears and laughter are never very far away." It's an astute assessment of Binoche's allure, though to it needs to be added that conspicuous intelligence and a steeliness that underpins that combustible emotion.

She had an international profile very early in her career, her breakout role in André Téchiné's Rendez-vous being quickly followed by The Unbearable Lightness of Being, Philip Kaufman's adaptation of Milan Kundera's acclaimed novel, opposite an equally up-and-coming Daniel Day Lewis.

Since then she's worked with many of the best, including Krzysztof Kieslowski (Three Colours: Blue), Michael Haneke (Code Unknown and Hidden), Olivier Assayas (Summer Hours, and last month's Cannes competitor Clouds of Sils Maria), Abbas Kiarostami (Certified Copy) and David Cronenberg (Cosmopolis). Few actors could boast her set of awards - an Oscar, Bafta and César, along with the actress prizes from all three major festivals (Cannes, Berlin and Venice) and three European Film Awards.

She's a workaholic, who declares that "I would feel exhausted if I was just relaxing on a couch." We've just seen her as a scientist in Godzilla, her first blockbuster, though she's had chances before, notably turning down a role in Spielberg's Jurassic Park in 1993. "If I'd had time I would have done it, because I'm a curious animal. But although I've had a lot of opportunities for, let's say, more commercial films in America, I have to be taken by the story and the connection with the director."

Godzilla director Gareth Edwards did impress her and, having passed on dinosaurs 20 years ago, she had a good reason for finally encountering this one. "I had to watch every Godzilla film possible with my son when he was a little boy. So this was a big win with him." Again she roars with laughter. "He's over the moon. Usually he's not that interested in my films.

Alongside Raphaël, who is now 20, she has a 14-year-old daughter, Hana (both from former partners; she has never been married.) Another recent film, A Thousand Times Good Night, in which she played a photo-journalist failing miserably to balance work with parenthood, unavoidably brings one to her own life. And she's happy to talk about it.

"I'm trying my best. It's a struggle. It requires a lot of back and forth to maintain your passion and maintain your family. I can't be a stay-at-home mother, that's not me, and my kids know that. But I try to go back home during filming, or they come to see me on set. And we speak every day.

"They have their lives also, their friends, and need to be in one place," she adds, referring to their home in Paris. "When he was little Raphaël always came with me. Then when he was 10, I said, 'You choose now, you can come with me whenever you want.' He was strong enough to decide for himself, and often preferred to be with his friends. My daughter is more inclined towards travelling, and adapting, than he was. So it depends on the personality of the child."

When we speak again, she's on the phone from Bulgaria, where she's filming Nobody Wants the Night, as the 19th century writer and arctic explorer Josephine Peary. This is just a few weeks after completing another real-life role in The 33, about the Chilean mining accident in 2010. Binoche plays Maria Segovia, sister to one of the miners, whose vocal presence at the tent city that grew around the rescue site earned her the nickname The Mayoress; it's a moniker that sort of fits the actress, too.

Occasionally Binoche finds time to appear on stage. And next year she will be making her first visit to the Edinburgh Festival, in a production of Sophocles' Antigone. She first saw the play when she was 20. "It has always stayed in my mind. It feels very contemporary, very political, especially in light of what's going on in the Middle East." She laughs again when she recalls that the poet Anne Carson, who has written the adaptation, had originally proposed that she play Elektra. "But Elektra wants to kill her mother - and I don't want to do that."

It's hard to believe that she's just turned 50. Her response to my raising the subject is typical of this no-nonsense force of nature. "I can't think about what time it is, just what I'm doing next."

I ask Binoche, a passionate painter, if she could empathise with Claudel, who couldn't practice her art for so many years. "It's hard to imagine what she went through. But when I don't work as an actor or painter, I always find ways of being creative. I feel that a relationship is a creation, in a way, with kids, partner, family, friends. Wherever you put your energy and imagination, your heart, is creative. Even though it may not seem like it, you can make your life an art form."

Camille Claudel 1915 opens in cinemas on June 20.