ON PAPER, the facts of Carla Bruni's life read like something ripped from the pages of a Jackie Collins novel. Born into great wealth in Italy and raised in a castle in Piedmont, Bruni moved to Paris as a child to escape the threat of kidnap. She was catapulted on to the catwalk in her teens and spent a decade as one of the world's highest-paid supermodels. She dated Mick Jagger, fronted campaigns for Chanel and Dolce & Gabbana, and by the end of the 1990s was earning millions of dollars a year.

But even Jackie Collins - no stranger to the outrageous plot twist - would have trouble explaining what happened next: Bruni walked away from modelling, shacked up with a French philosopher and embarked on a second career as a songwriter of no little talent and, if her second album No Promises is anything to go by, no little ambition. All of which makes people want to hate her even more, I imagine.

In person, hating her is difficult. She is easy and friendly, though I suspect her confidence in the company of strangers is born of a single long-held belief: that being thin, stylish and tall brings a natural authority.

In comparison I'm reminded of a story Naomi Campbell once told about being bullied by girls at her school for the same crime. She was forever crossing roads to avoid passing bus stops, she said. Of course Bruni went to a Swiss finishing school, Campbell to a Streatham comprehensive; still, I can't imagine the Italian ever being so uncomfortable in her skin. She certainly isn't now, at the grand old age of 39.

We meet in Claridges, the plush London hotel. The day is hot, even Bruni thinks so. We start with small-talk, in this case today's French presidential elections. Bruni still lives in Paris, with her philosopher partner Raphael Enthoven and their five-year-old son, Aurelin. She can't vote because she's Italian, but she has her opinions nonetheless. I ask her for them: Sarkozy or Royal?

"Ah, Royal," she says, like it's a no-brainer. "I really don't like her but I would always vote on the left. My parents always did too. It's like a tradition. I would never vote on the right. I would vote in the centre, maybe, but Bayrou, who was in the centre, has gone now."

She is proud that she helped vote Berlusconi out of office in Italy, though. "Ah, Berlusconi," she says, shaking her head. "Italians are just not into politics for some reason. I wonder why. Every country is like a person with a special temperament, I suppose. Do you mind if I smoke?"

I don't, and she lights a cigarette so thin it's hardly worth wasting a match on. "I smoke when I work or just before a gig," she adds. "It's because I get worried. I think I should quit. If I have another child I think I will."

Jane Birkin, who knows a thing or two about singing, has said that Bruni has a voice like a truck driver. It's a compliment, of course, and Bruni takes it as such. "I do have a very husky voice," she says.

A throat specialist told her that to use her voice like a proper singer she would need to be a little larger. Opera size, perhaps. "I would need a much larger waist," says Bruni, cinching that part of her anatomy with both hands and throwing out her chest. "For me to go haaaaaaaaa" - she sings a high pure note - "is quite hard. It's easier to go huuuuuuuuuuh", and she lets loose a beguiling low-frequency whisper.

It's sounds like that which helped her first album Quelqu'un M'a Dit sell over a million copies in France alone. If you haven't heard that record, seek it out. It's very good. I can remember it landing on my desk and thinking: "Not that Carla Bruni, surely?" At that point Bruni was best known as the supermodel who had conducted an on-off affair with Mick Jagger. Tabloid femme fatale, perhaps, but budding chanteuse? Unlikely. Mine was a not uncommon response.

In fact, Bruni wrote almost every word and note, and has been playing guitar since before she was in her teens. Even in the busiest of her modelling years, she rarely travelled without the instrument. "Modelling is a lonely job. You're always travelling around and alone in a hotel room. So the guitar would be great company. But it was only ever that - company. I never thought I would be good enough to work with it."

Having ended her modelling career, Bruni took up her music seriously. She began to learn the cello and to gather the scraps of lyrics she had acquired. She made a demo tape of her songs and took it to an agent she knew. She won't pretend her name didn't open doors but, as she says: "Modelling gets you in, but once you're in you better be good. Or at least real. So since I wrote everything, I was holding on to that to give me a little credibility." Her agent went one better, sending the demo tape to French record label Naive, but refusing to tell them who the singer was. They were impressed enough to sign her unseen.

For No Promises, her second album, Bruni has written music to accompany a series of poems by Emily Dickinson, WH Auden, WB Yeats, Dorothy Parker, Christina Rosetti and Walter de la Mare. It sounds fantastically pretentious - and very French - but again she makes it work.

She sings in English this time and if there's a unifying theme to her chosen poems it lies in her subconscious, she thinks. In other words she can't put a name to it. But she's aware that all three of the women writers led lonely lives and that many of them deal with ageing.

The choice of poems was very deliberate, however. "Yeats wrote some wonderful poems that are like beautiful songs but sometimes you can feel the man behind them and they would be hard for a woman to sing," she explains. "So the poems I chose are the ones that were the most simple to me and which I understood right away."

It's a sombre album with a sombre coda: it is dedicated to the memory of her brother, Virginio Bruni Tedeschi, a graphic designer who died of cancer in July 2006. "He was seven years older than me," she says. "I never knew the world without him. He was ill for a long time, about 10 years. But then he got this very bad lymphoma which killed him in two weeks. His wife was at the hospital when he died. He died in her arms."

Nothing about Carla Bruni's late change of career should be that surprising. Her Italian father, heir to an industrial fortune, was a composer and her French mother a concert pianist. Her elder sister, Valeria Bruni Tedeschi, is a noted Italian actress who has worked with Bernardo Betolluci, François Ozon and Ridley Scott. She is also an award-winning film director in her own right.

The family pile is Castello di Castagneto Po near Turin. It was bought by Bruni's father, Alberto Bruni Tedeschi, in 1952 and refitted to his tastes. These extended to restoring ancient frescoes, installing exquisite parquet flooring and scattering antiques everywhere. Carla Bruni's infancy was spent in a wonderland of crystal chandeliers, Renaissance sculpture and landscaped terraces teeming with lemon trees.

In the early 1970s, however, the family swapped Italy for Paris. At the time, Marxist terrorist organisations such as the Red Brigades were active and kidnap was a real and present danger. In 1973 John Paul Getty III was grabbed in Rome and held captive for several weeks until his family handed over $2million in ransom. Famously, he also lost an ear in the process. Five years later, the politician Aldo Moro was kidnapped and murdered by the Red Brigades. The 1970s weren't a good time to be a rich, high-profile Italian.

So Bruni was raised in Paris then packed off to boarding school in Switzerland. The family moved back to Italy in the 1980s but she returned to Paris to study architecture. When Virginio's then-girlfriend suggested she try modelling, she dropped out and began a career that would last more than a decade. The magazine Business Age put her in the top 20 list supermodel rich list and estimated her earnings in 1998, her last full year as a model, at $7.5m.

Bruni left the catwalk, she says, "when the modelling started to slow down". She was also tired after what she describes as "10 years of running around". There may have been other contributing factors: her brother's illness was diagnosed around this time and, in 1996, her father died.

Castello di Castagneto Po is still owned by the family but with her father gone and her childhood years there a memory, Bruni has little emotional connection with it.

Neither, it seems, does her mother, who plans to sell the building. Two months ago she started the process by auctioning off its contents. Christie's handled the sale. There were around 300 lots, mostly 18th and 19th century furniture and paintings, and they fetched £12.7m, well above the £7m pre-sale estimate. The money will be used to establish a foundation in memory of Virginio. It will make four sizeable donations a year to medical and humanitarian causes.

Does Bruni feel any guilt about her pampered upbringing? "Not much," she says. "I started working when I was 18 and never asked for anything else from my father after that. I never got any money. My sister and brother were the same. Our parents educated us with other values than money. Of course, compared to people who have a hard time in life, we were really privileged. But when I was modelling I met wealthy people and I realised that I was not like them. I had the impression we were lucky but not like one of those families that only cares about money."

I ask her about the apparent ease with which she appears to have coasted through life, from gilded youth to supermodel to rock star arm candy. If she is genuine about furthering her career as a musician - as an artist - doesn't she feel the need to experience some form of struggle? Instead everything seems to have been handed to her on a plate.

"Nobody avoids problems in life no matter what social position they have. Struggle comes from losing people and I've lost a lot of people. So I think I have had struggle. People have died. There was never a long period of time without a funeral."

It's a mordant note for such a sunny day so we leave it and talk about Paris. Bruni and Enthoven used to live in St Germain, on the trendy Left Bank, but they have recently moved to a house in the 16th arrondisement. It lies west of the Seine and near to the Bois de Boulogne, the massive parkland loved by the impressionist painters.

The photographs for the liner notes on No Promises were taken chez Bruni. They show close-ups of children's toys, vases of roses, Bruni in a white shirt silhouetted against a French window, and perched on a chaise longue. On the cover, she sits reading poetry in a babydoll nightie; poised, elegant, cool.

They add a neat personal touch but they underline one salient fact: that this is not a woman with demons. She will never play the cello like Jacqueline du Pré or perform like Janis Joplin, even though she tells me she would like to. Does it matter? Not a bit.

"When I was a child I didn't think about being a musician as a career," she tells me, "but I thought about it as a dream."

With a third album of Italian songs already in the pipeline, it's a dream she's not about to wake up from any time soon.

The album No Promises (Pramatico) is released tomorrow