Everybody knows that supermodels don’t fit the dumb-blonde stereotype: in fact, these days it’s difficult to find one whose beauty isn’t backed up by formidable brains. But while you can discuss human rights with Bianca Jagger, Eastern philosophy with Christy Turlington or social and political science with the bright young British model Lily Cole, when conversation turns to the late verse of William Butler Yeats, there’s only one woman worth listening to: Carla Bruni.

The French-Italian supermodel-turned-pop star is perched on a scruffy sofa in the Covent Garden Poetry Café, singing the praises of the Irish bard, two of whose poems feature on her new album, No Promises (released in the UK next month). Each song on the album is adapted from a poem, with Yeats, W. H. Auden, Christina Rossetti, Emily Dickinson and Dorothy Parker all providing words for Bruni’s intimate, quivering voice and folky guitar. On the cover she is neither staring sultrily nor strumming sensitively (the stock female solo artist poses), but sitting on a cushion, absorbed in a book of verse.

On this side of the Channel Bruni is best known not as an ambassador for poetry but as a serial celebrity-seducer: she was Mick Jagger’s “other woman” during his marriage with Jerry Hall, and has been romantically linked to both Eric Clapton and Donald Trump. In France, however, her music career has eclipsed her colourful past: Bruni’s first album, Quelqu’un m’a dit , in 2003, was a surprise hit, with national sales of 1.2 million. So why, now, is she ditching popular chansons for dusty old quatrains, and risking her new-found success?

Bruni, whose superhumanly sculptured features are undiminished at 39, admits that there was resistance: “Everybody was like, ‘What? Poetry from the 19th century?’ The record company thought it was suicide.” But having fallen in love with a handful of poems, Bruni couldn’t stop herself: she began to weave tunes around them, and “ petit à petit ” the project grew into an album. Using verse in English was a conscious, if unpopular, decision. “The French say: ‘Why didn’t you use French poetry? We have the best poets!’ But English has a rhythm and a sound that is made for songs,” she argues.

She uses that rhythm well, turning key verses into refrains and teasing the poems out into laid-back pop songs, in which her pleasantly smoky half-whisper (somewhere between Marianne Faithfull and Isobel Campbell) is accompanied by tasteful, unobtrusive guitar and harmonica. Musically, No Promises doesn’t break any new ground — it shifts between jazz, blues, folk and country while never straying far from Norah Jones territory — but it’s a daring concept and, remarkably, it works.

There is a tradition of adapting poetry in Italy and France, Bruni points out: Léo Ferré sung Rimbaud and Verlaine’s poems in the 1960s and Fabrizio De André adapted the American poet Edgar Lee Masters’s Spoon River Anthology . But the Brits are less used to pop upstarts messing with their poetic heritage. “I hope the purist is not going to mind,” she says, in her musical, drawn-out accent. “Now that I am in England I am a bit worried . . .”

Bruni has another reason to be anxious: as we talk, the contents of her childhood home, an 18th-century Piedmontese castle, are being auctioned off at Sotheby’s to benefit a charitable foundation set up in honour of her brother Virginio, who died last year. The items, acquired by her father Alberto, who was a passionate antiques collector, fetched £12.7 million — the highest total for a private collection of decorative arts that Sotheby’s has recorded.

The Bruni family is, as you might have guessed, not short of a bob or two. But their wealth, which comes from Alberto’s father’s tyre-manufacturing company, hasn’t always been a blessing: in the 1970s it made them a potential target for the terrorist Red Brigades, and when Carla was 7 they fled to Paris.

Whether in France or Italy, their homes were always full of music: Alberto, a composer, would write at his piano while his wife Marisa, a concert pianist, would practise at hers. Carla learnt the piano and violin as a child but it wasn’t until, aged 9, she picked up a guitar that she really fell in love: “From the minute I had it I played it every day.”

Even after she became a model at the age of 19, she kept strumming away: “I was always imagining being a musician, and then modelling was a very funny parenthãse .” Some parenthãse : in Bruni’s 12-year career she modelled for Guess, Dolce & Gabbana and Chanel and made enough money to qualify for the Top 20 supermodel rich list in Business Age . And, thanks to her affair with a certain Rolling Stone, she was a regular tabloid fixture, usually portrayed either as a schemer arranging for paparazzi to snap Jagger leaving her flat or a catty rival claiming that Jerry Hall had “no class”.

Spending time with rock stars might have been exciting, but it did not inspire her creatively. “It would have been even more difficult for me to write music if I was married to a musician.” Instead, Bruni found herself a young French philosopher, Raphaël Enthoven.

Unfortunately, like Jagger, he came with a certain amount of baggage: namely Justine Lévy, daughter of the philosopher Bernard-Henri Lévy, and Enthoven’s former wife. Soon after Enthoven left Lévy, she wrote a venomous novel, Rien de Grave (Nothing Serious), in which Paula, a silicone-enhanced model-turned-rock star, steals the protagonist’s husband. When the book was published in 2004, it didn’t take a master code-breaker to work out that Paula was Carla by another name.

But by then Bruni, whose modelling work had dried up in 1998, had returned to her true calling — music — and was in a more contemplative mood: “After all these years of running around, I finally had the empty time that I needed to write songs.” And with that “empty time” came poetry, and the idea for No Promises .

Before recording the album, she enlisted the help of her friend Marianne Faithfull, who spent two months guiding her study of the poems. “I had to call her ‘my dear professor’. We looked at the biographies of the poets. Marianne showed me the letters between Yeats and Maud Gonne.”

It is Yeats (or “Yeets”, as Bruni charmingly refers to him — along with “Owden”) who begins the record, with Bruni’s most daring choice, Those Dancing Days are Gone . Despite its sunny refrain, this is a poem about old age that involves “wrapping that foul body up/ In as foul a rag” — lines not, perhaps, written with the supermodel in mind.

His second poem on the album, Before the World Was Made , is a better fit. A woman argues that her artificial self — made-up and flirty — is actually more authentic than her natural one; a sentiment that chimed with Bruni’s experience of the modelling world, in which she “found artificial things in the deepest situations, and the opposite, too”.

There are other personal echoes. Christina Rossetti’s Promises Like Pie-Crust , for example, captures the pragmatic tone of a woman like Bruni, whose romantic history will never be fully revealed: “Promise me no promises . . . For I cannot know your past,/ And of mine what can you know?”

Now edging into middle age, Bruni has had occasion to look back on her eventful life and carve out something of a personal philosophy. Of all the poems on No Promises , Dorothy Parker’s Ballade at Thirty-Five expresses it best: a song of experience from “a lady who/ Followed ever her natural bents”, it could have been written for Bruni herself. “When I have to choose,” she explains, “I always choose doing things, so I make great mistakes but I don’t have regrets.” Between regrets and mistakes, she adds, with a pleased little laugh, “I would choose mistakes”. No Promises is released on May 7 on Dramatico Entertainment

Fashion and pop: a two-way street?

Karen Elson The 28-year-old Mancunian proponent of “freak chic” duetted with Cat Power, co-founded the hip cabaret troupe the Citizens Band and even wed Jack White.

Kate Moss Having previously dabbled with Primal Scream, the waifish one is now writing songs with her beloved Pete Doherty — to the irritation of Babyshambles, who see her as Yoko Ono Mk II.

Victoria Beckham Made her debut on the catwalk for Maria Grachvogel in 2000; since then Posh Spice has concentrated on her fashion designs — and fragrances.

Bryan Ferry “They’re great old-fashioned British brands,” said the former Roxy Music frontman of Burberry and Marks & Spencer, both of whom he has modelled for.

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