Nymphomaniac actress Charlotte Gainsbourg on starring in one of the most explicit films ever: It was so embarrassing to perform

The 43-year-old actress discusses her role in the controversial Lars von Trier project and having the right profile for Hollywood

French without tears: Gainsbourg says she was embarrassed when shooting ‘Nymphomaniac’ (Rex Features)

'I know people don't think of me as somebody very funny!" says Charlotte Gainsbourg, with a quiet smile. It's true; just take a glance at some of her credits – from 21 Grams to I'm Not There to her trio of Lars von Trier movies, Antichrist, Melancholia and last year's sex-odyssey double-header Nymphomaniac.

She's not exactly Melissa McCarthy when it comes to mirth-making. "I like relating to some kind of uneasiness," she says. "Even in a comedy, it's quite nice to be able to have a dark side."

It's almost impossible to imagine that Gainsbourg has "fun" when she's acting. Right back to 1993's The Cement Garden, the movie of Ian McEwan's novel of incestuous siblings directed by her uncle Andrew Birkin, she has been dealing with taboo subject matter. She seems drawn to women in crisis. "I've been uncomfortable for many, many years," she explains, sipping herbal tea. "I feel less uncomfortable… I think it's easier for me now. But I relate to being unstable." She pauses. "I don't know why."

You might easily point to her background, as the daughter of late French pop icon Serge Gainsbourg and English actress Jane Birkin. Her famously provocative father caused outrage when he directed her in the 1986 film Charlotte For Ever and the video for their song "Lemon Incest", both featuring her scantily clad.

While she also spent her teens playing a series of angst-ridden adolescents, from her debut in Paroles et musique to Claude Miller's 1985 film L'Effrontée, Gainsbourg does not come across as the sort who looks like she's spent years in therapy. "I think I protect myself quite well," she nods. "I feel quite stable in my roots and what I go back to. Of course I could say my family, my children [she has three], Yvan [Attal, her actor-husband, with whom she's been since 1991] – yes, that's very solid. But, yeah, I feel quite rooted, pretending to not be!"

The conversation inevitably turns to Nymphomaniac, Gainsbourg's eye-watering turn as the sex-obsessed Joe. In the next fortnight, the full five-and-a-half-hour version will be available for the first time to UK viewers on Blu-ray. "I prefer the long version," she says. "That's the first one I saw. To me, it's really Lars's film. It's his taste and his rhythm and everything he worked for." Was she ever shocked? "The sex was not shocking at all. It's necessary for that story; that's what we need to see. I saw a lot of beauty inside the brutality and inside the crudeness of the sex he's showing."

Double bill: Kookie Ryan, Charlotte Gainsbourg and Papou in ‘Nymphomaniac’ (Christi an Geisnaes)

She still recoils at the thought of some scenes, notably between Joe and Jamie Bell's sadist, which saw her strapped to a sofa and caned. "It was so embarrassing to perform," she says. "I wanted to do it, but at the same time I wanted to hide."

Samba came in a rush of four films that Gainsbourg took on in the wake of Nymphomaniac. "It was all mixed up – four very, very different characters," she says. Alongside playing Alice, she took on an unfaithful sibling in Benoît Jacquot's 3 Hearts (due in the UK in August), a volatile Italian mamma in Asia Argento's Incompresa and a grief-stricken mother in Wim Wenders's 3D melodrama Everything Will Be Fine, a two-part shoot that book-ended all the other movies. "We did all the summer scenes at the beginning and all the winter scenes at the end," she explains.

Now 43, Gainsbourg has faced death herself, after suffering a traumatic injury while water-skiing in 2007. After suffering a seven-day headache, a visit to the doctor led to the discovery that her brain had been pushed to the side and her head was filled with blood. "I got very scared afterwards," she recalls. "You get this thing of, 'thank God I'm still alive', but it doesn't last for very long. I was never a hypochondriac before – its gone away now – but I got quite scared of everything. The strangulation [scene] in Antichrist, I thought my head would pop!"

She channelled a lot of these feelings into 2009's IRM, the third studio album – produced by Beck – in her on-off music career. While she subsequently released Stage Whisper, a double album of live tracks and unreleased songs from IRM, there's been nothing original since. Will she record again? She nods. "Because I did those four films, really in a row, completely together, I didn't have a minute to think about music. But now, yes." She's hugely modest about it all. "It is a challenge because I don't value myself very much with the music," she says. "I don't value the results as much."

Charlotte Gainsbourg in her new film Samba (David Koskas)

Gainsbourg has never ventured towards Hollywood. There was a point when she was set to make Terminator Salvation, but had to pull out due to scheduling conflicts with Antichrist. "I would've loved to do both," she says. "I don't know if I have the right profile for big American films – I'm not really sure – but they have lots of directors that I adore."

Yet shortly after we meet, it's announced that Gainsbourg has joined the cast of Independence Day 2 – the sequel to the 1996 alien-invasion film. Gainsbourg's inclusion (in an as-yet-unspecified role) is a surprise. But she has been spending more time in LA, what with recently launching a fashion line with cult denim brand Current/Elliott.

In the meantime, she has been shooting Oppenheimer Strategies, a US indie co-starring Richard Gere, set in the world of politics. Back to the day job, then, far removed from the romantic comedy of Samba. For her, it's not about laughter or tears but total immersion. "I love the idea of diving… not really into a character – I never lose myself – but diving into an ambience, an adventure," she says. "That's something that I miss if I don't do it."

'Samba' is in cinemas now. 'Nymphomaniac: Volumes I & II – The Director's Cut' is available to buy on Blu-ray from 11 May