Have you met Miss Norah Jones?

She appears famous enough, at first, when we meet in Paris, where she is on tour not to perform, but to talk about her acting debut in Wong Kar Wai's latest film, My Blueberry Nights. The sultry, moody face, familiar from the billboards, dissolves when she relaxes. Up close, she's petite, at 5ft 1in tall, and pretty, with a throaty laugh.

"I found filming scary," she admits. "I am used to being in control - of the music I write and record, and what I say about it. With a film, you hand all control to others - the writers, the director, those behind the camera and even other actors. I am just part of the process, rather than the person who makes it happen."

It probably didn't help that her name is writ large above the title and those of other well-known actors, including Jude Law, Rachel Weisz, Natalie Portman and David Strathairn. Or that the man directing her debut is famous for making In the Mood for Love. He called Jones's manager and simply invited her to play his lead in a new project.

"I had never heard of him," Jones says disarmingly. "So I watched In the Mood for Love, and thought it was amazing. We finally met up, and he is this very tall guy, with dark glasses, looking very odd. He was sizing me up. After a time, he said, 'Well, Norah, do you want to act?' I said, 'I don't know whether I can, but I can try my best.' " The film is a whimsical tale that starts with Jones's character, Elizabeth, being dumped by the love of her life. She confides her heartbreak to the owner of the cafe (Law) where she and her lover regularly rendezvous. She then decides to travel across America to look for a new life, waitressing to make money. Instead of receiving help and encouragement from those she meets, she becomes a shoulder to cry on - for a troubled policeman (Strathairn) and his eccentric wife (Weisz), then a crazed and desperate gambler, wonderfully played by Portman. Elizabeth realises there are others suffering far deeper loneliness and emptiness than hers. The film becomes a classy, if slow-moving, road trip to salvation, from New York, to Memphis, to Nevada, California and along the legendary Route 66.

The film opened the Cannes film festival, not the easiest crowd to impress. But they were smitten. Even The Hollywood Reporter trumpeted: "The glue here is Jones, who holds a wispy, wistful film together with a deeply felt, unselfconscious performance that strikes the right notes without ever falling into repetition or banality."

Jones isn't so sure. "I didn't know what I was doing, and felt really stiff in the first few scenes," she says. "That was just as well, because the film was filmed in sequence, and my character had to appear unnerved after being dumped. She would have been uncertain about what to do next. That was exactly how I felt on the film."

Her own boyfriend, the bass-player Lee Alexander, has also been lost along the way. But this is by her own choice. "We have worked together, lived together and been on the road together," she says. "We have known each other for seven and a half years, which is one quarter of my life. We complemented each other because we are opposites. But it was not enough, and it had just run its course."

Like her film character, Jones is about to embark on a road trip, to relax, see the world and dream up new songs. "I have worked nonstop for the past seven years," she says, "on albums, tours, promotions and the film, of course. The temptation is to carry on going while the demand is there. My record company wants a new album, and there have been other film offers. But I look around and see a lot of unhappy performers. Maybe too much is demanded of them."

Which brings us back to her father, now something of a musical legend at 87, and Harrison. "George was always looking for an alternative to fame. He needed to play and write, but enjoyed so many other things, too. He was a deep thinker and could not comprehend why people seemed to want a piece of him. He let the music do the talking and avoided being on show." But she is sympathetic to those who fall by the wayside. "I feel for Britney Spears," she says. "In other circumstances, that could have been me."

Jones, christened Geetali Norah Jones Shankar, grew up with her dancer mother, Sue Jones, who is 30 years Shankar's junior. Mother and daughter moved to Dallas, Texas, after Sue broke her ankle and was forced to retrain, first as a film-script supervisor, then as a sales executive for an estate agent, and finally as a nurse. It is clear that, although Jones might have inherited her talent from her father, it was her mother who taught her self-reliance and the benefits of hard work.

"She was a 1960s hippie, with flaming red hair," Jones reports. "She now has gorgeous white hair, and is stunning. We are not at all alike, and bicker a lot. But I am proud of her. She worked hard to bring me up the right way - just the two of us, living together."

Jones became known, initially, as a sultry girl with an amazing voice who played in bars around Dallas. Then, at 19 she left home to move back to New York. She sold her 1971 Cadillac to finance her trip, met up again with her father for the first time in 10 years and got a job, just like her character, as a waitress.

"I waited tables for a couple of years," she says. "I was at the cafe in the Metropolitan art gallery, combining it with the occasional gig. I worked for two dollars an hour, plus tips. So, 50 bucks a shift was pretty good. I rented a loft apartment in Jones Street, of all places. But money was thin and I rapidly used up my savings."

She kept up her writing and rehearsing, and hooked up with Alexander, whom she met over the tables when he, too, was doing a stint as a waiter. And her sensual sounds, with a mix of soul, jazz, folk and country, seemed to strike a chord. Her debut album, Come Away with Me, made her name and fortune, and she swept up Grammy awards the following year.

Her father became a fan, and she cannot speak highly enough of him. "He was already a well-known composer at my age, but that was back in 1948," she says with some wonder. "He could not be with me all the time when I was growing up, and I don't have any regrets. The fact that we are close now is great."

Jones has that rare ability, like all special songwriters, to compose quickly, never truly knowing where the words come from. She wrote the title track for My Blueberry Nights, a four-minute song called The Story, which she completed in not much more time than it takes to listen to. "We were doing a night shoot on the film in New York, and I came home at 6am," she says. "I was not tired, so went into my piano room, which faces east, and watched the sun come up. It was such a beautiful sight, the song wrote itself."

She was also asked by Wong to pick songs that would match the various locations. So, the music for the movie includes some of her favourites: Ry Cooder, Cat Power, Otis Redding, Ruth Brown. "The director then used the music to set the mood of certain scenes," she says. "It relaxed me - and the other actors seemed to enjoy it, too."

Jones needed to be relaxed for an erotic kissing scene with Law. It took three days to film. "It was not your typical kiss," she says. "He had to kiss cream off my face, from every angle, so they had to keep applying sweet cream for each take. He must have eaten a gallon of the stuff by the time we finished." Jones gives one of her throaty laughs. "I was lying down, being kissed by Jude Law," she says. "I thought, 'If filming is always like this, I will definitely do another one.' "

My Blueberry Nights opens on February 22; the soundtrack is released on February 25