Every generation has its French-language hit. In the Sixties, Britain was seduced by Je t’Aime, Serge Gains bourg and Jane Birkin’s mantra of steamy Gallic sighs. The late Seventies brought high-speed Belgian punk – Plastic Bertrand’s Ça Plane Pour Moi, and then in 1988 Joe Le Taxi drove to No 3, sung by the 14-year-old Vanessa Paradis. For those who were at school at the time, the song was a revelation. We studied the lyrics in our French lessons, and the cute girl singing it seemed to embody all those French expressions we had been learning, with her “ insouciant” dancing in the video; flicking her hair with a certain “je ne sais quoi”. And she was only 14! [[ Yet while Paradis was pretty much a one-hit wonder in this country, she’s gone on to become France’s reigning queen of chic.

Today, with a stack of movies also under her belt, she has just released her fifth album, her first in five years and third No 1 seller in France in a row. Oh, and she’s shacked up and procreated with some actor called Johnny Depp, who has bought his new family an island in the Bahamas, but more on him later.

At the grand old age of 34, she may be about to revive her fortunes in Britain, as word about her new record, Divinidylle, spreads. “People’s reactions are so beautiful,” she agrees, sitting in a hotel room in Paris, her blonde hair rolling around her face in endless messy curls. “I am so glad.”

Listening to the album, the first thing you notice is that her voice really hasn’t changed much – that babyish edge is still there, though in an understated, rather than cutesy, manner. The songs, all in French, are beautifully melodic: Junior Suite is a, haunting, melancholic pondering on the constancy of the sea and of love, while Chet Baker is more upbeat and rocking. The album ends with Jackadi,a gentle song for Paradis’ five-year-old son Jack, which includes snippet of his own gurgling babytalk.

Paradis co-wrote much of the album with the songwriter Matthieu Chedid, with whom she duets, Gainsbourg style, on a rather 1960s cheeky pop number, Les Piles.

Indeed, she is a huge fan of Serge Gainsbourg, with whom she recorded an album, aged 16. She has beautiful memories of “spending afternoons at his house listening to his stories. He told a bunch of stories about many years before, fun stuff, crazy stuff, forbidden stuff.”

Was she in awe of the great man? “Oh yes! Serge is our precious diamond here in France, so I couldn’t believe my ears when he wanted to work with me, I was amazed. I was so impressed that I didn’t want to embarrass him with it – so maybe I kept cool too much.”

Ah yes, the cool factor. While she may have been affecting it in her teens, today she is more naturally self-assured. The coolness, though, has slid over into frostiness – personal questions are off the agenda. An inquiry about whether her kids have done anything that made her laugh recently leads to a stern rebuke. “This question is way, way too personal,” she declares, her huge round eyes flashing. To us it may seem odd, but then the French expectations of privacy from the media are much higher. Of course, there is also a particular sensitivity regarding her daughter. Lily-Rose Melody Depp, born in May 1999, made the headlines this year when she was rushed to hospital in the UK after falling ill with a mysterious, seemingly life-threatening, illness, while her father was filming in this country. It is now thought the seven-year-old suffered kidney failure after an infection. Her father said after her recovery: “To say it was the darkest moment, that’s nothing. It doesn’t come close to describing it.”

Paradis settles for telling me that having children is “the most beautiful thing in the world. They are honest, they are real and your love for them keeps growing... Is there anything that can compete with that? If you find it, let me know.”

She also admits that her daughter looks set to be a musician, which her maman is delighted about – though she hopes Lily-Rose will be older when she makes it. “I would love her to wait a little longer than I did.”

Paradis thinks she has avoided the usual child-star pitfalls by having supportive, loving parents. “I’ve been really well advised. And lucky. It’s an exceptional road to be able to take: to sing, or act. But it’s not obviously the best construction for a teenager growing up – the values are changed, so you have got to kind of make...” she laughs because she can’t find the word. “Le tri, trier. To sort! Yes. To make sense of right and wrong.” She laughs again. “I mean, I seemfine, but I might be completely wrong and blind! But I think it went pretty OK for me.”

Yet a film she made, Noce Blanche, for which she won the 1990 César Award for Most Promising Actress, showed her as a teenager having an affair with her philosophy teacher. Many years later the director, Jean-Claude Brisseau, was sentenced to two years probation for sexual abuse of minors – actresses, in fact. Typically, Paradis has never spoken about it. The subject is out of bounds today. She claims never to have been exploited in her youth. “Oh I was naive! Yeah I was naive! But that didn’t stop me making decisions.” Subject closed.

As for new films, she is irked when I mention Hollywood. “This is too much of a set-up. By Hollywood do you just mean American movies? Because if you mean blockbusters, every country has those. I’m not against making any good movie, let’s put it that way. And there are amazing people in the States. I mean they have Jarmusch. They have Scorsese. Pirates of the Caribbean is a blockbuster but it’s a great movie.”

It’s also the film that gave her partner – she and Depp have never married – ultimate mainstream approval, after a life starring in weirder works. He met Paradis, in a hotel lobby in Paris, when she was 25 and he 34. “Our story is love and friendship united,” she told Elle. “I have the impression that no one could love the way we love.” His painting of her, wonky front teeth and all (her beauty is refreshingly imperfect close up), adorns the cover of Divinidylle, a title that she says refers to the glorious start of a relationship.

And the secret of staying that way in a long relationship? “Well, never take anything for granted. Once you think that the person is there for ever, then there’s no efforts. Everything is constantly growing and you have got to keep your eyes open. Lots of respect, lots of listening... It’s still hard to keep it going, you know?” She laughs. “But if you walk in this direction, then romance is the cherry on the cake.” Her gateau looks pretty well-stacked to me.

Divinidylle (Wrasse) is out now

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