ANYBODY who was at the City Halls last June to witness Madeleine Peyroux’s return to Glasgow after a decade’s absence will remember that it was an extraordinarily moving experience; the sort of five-star concert experience that doesn’t come along very often.

The American singer-songwriter with the sultry, bluesy voice held the audience in the palm of her hand and there was a strong sense of solidarity when she made reference to the political situation in the States and took the mickey out of its president.

Little wonder, then, that Peyroux remembers her one Scottish gig of 2017 clearly when we speak on the phone to discuss her next one – in Edinburgh later this month. But what is a surprise is just how much of an impression that June day in Glasgow made on her, and how it played a part in the way she approached her new album, Anthem, which is the catalyst for her current European tour.

Reminded of that concert, the 44-year-old immediately responds: “That was a memorable visit to Glasgow. It changed me. It was a big part of my growing up. Before the concert, I met some Glaswegians out on the street and they started telling me about their personal lives – two blokes, two fans, told me about some very serious, tragic things that they had gone through. It was very generous of them; it was a real human connection and it made me think very deeply about how I’ve got to be open to that all the time. I have to assume that people want to talk about the hardest things; I shouldn’t shy away from it. I should be open to these conversations.”

It’s little wonder that anyone who has followed Peyroux’s career or is familiar with her recorded output through which run recurring themes about alcoholism, homelessness, falling foul of the law and romantic disappointment should feel that she is approachable and ready to listen. This is the woman who began her performing life as a busker on the streets and metro lines of Paris and who told The Herald in 2009 when she was promoting her first, painfully honest, album of original material that she had “spent a lot of time with sadness”.

So how did the Glaswegian experience impact on Anthem? “I realised that the conversation needs to be on a personal level.” The conversation to which Peyroux refers is about the current political situation, a subject which may have united her with her Scottish fans but which is a thorny topic in her homeland.

The seeds for the album were sown during the 2016 US elections when Peyroux was touring the length and breadth of the States, getting a sense of her country and trying to find ways to connect with audiences who don’t necessarily hold the same views as she does.

Does she have to watch what she says about President Trump in the States? “Yes. The new record was definitely inspired by concerts where I found that I wasn’t able to talk about issues properly and couldn’t find the repertoire that reflected what was in the air – especially in 2016. I’ve realised that it’s not necessary for me to say anything more about him. He gets enough attention and he thrives on any sort of attention.

“The conversation needs to be on a more personal level so I decided to embrace speaking through the music only. The songs here are based on what’s happened – there’s Lullaby which was inspired by the image of a refugee in the ocean, and Down On Me was inspired by the financial paradox one finds oneself involved – one can’t get back on the horse if one falls off. Songs are meant to speak, and these are deliberately not preachy.”

The record is a group of stories of different people’s experiences and presents an intimate view of politics – through the prism of the personal. “The idea of writing new songs was at the back of my mind at the same time as I was invited to be part of a songwriting session where five of us were stuck together for a few days at a time in LA over a course of a year. It got to the point that I was really excited and wanted to record the songs right away; they felt so connected to what was going on. We recorded it last fall.”

The sessions were the brainchild of Larry Klein, the acclaimed producer with whom Peyroux had collaborated on four albums, including her 2004 breakthrough chart-topper Careless Love and, most recently, her 2013 foray into country music, The Blue Room. Peyroux found it particularly exciting to be writing the songs with musicians, “instruments in hand”, and hearing the songs – which span the musical genres from Marvin Gaye-like We Might As Well Dance to the bluesy funk of Down On Me – come to life.

Unlike her masterful 2009 album Bare Bones, which Peyroux wrote mostly with one collaborator per number, the songs on Anthem were mostly been born out of these afternoon jam sessions. She says: “I was the catalyst for those songs and I used the skills of partners, such as David Baerwald, to finish them.”

An exception to that was All My Heroes, an unblinkered but touching homage to some of the 20th century pop icons who have died in the last few years – “All my heroes were failures in their eyes/Losers, drunkards, fallen saints, and suicides.”

Peyroux explains: “The day after one of our former poet laureates died, David came in to the session bemoaning the loss and said ‘Let’s write something about that.’ So the song was inspired by all these great people we’ve been losing like David Bowie, Prince, Robin Williams, and also I had lost a dear friend, so it felt like the natural time to try to address this feeling of loss. So it was David’s idea and it changed form several times.”

Indeed, Robin Williams was one of the heroes Peyroux said, back in 2009, “made my life bearable when it was unbearable.”

It was, appropriately, a recently deceased hero of Peyroux who provided the title number – one of only two non-original tracks on the CD. Despite being a fan of Leonard Cohen, whom she knew originally as the father of a classmate from the American School in Paris, for years – and having previously recorded two of his songs – Peyroux hadn’t heard Anthem until Klein, who thought it fitted in well with how they were feeling about the political situation, brought it to her. She quickly became obsessed with it and with working out how she wanted to perform it.

“The stand-out line in the song,” says Peyroux, “is – ‘There is a crack in everything/That’s how the light gets in’. It has this power of hope. He’s saying: ‘Look at how terrible this is and then live through it and come out the other side.’ It’s really become a personal anthem, and I felt that it tied together all the stories on the record so it had to be the title song.”

Madeleine Peyroux plays Edinburgh Festival Theatre on Sunday November 25. For tickets call 0131 529 6000 or visit http://www.capitaltheatres.com. Anthem (Decca) is out now