Jane Birkin, Barbican, London

Out of the shadows of two husbands and 'Je T'aime...'

It says everything about cross-channel culture clashes. The late Serge Gainsbourg, a musical situationist who could switch from jazz to reggae to pop erotique and once told Whitney Houston, "I want to fuck you" live on French TV, is known in the UK – if at all – for three minutes of panting noises on his 1969 hit "Je T'aime... Moi Non Plus".

His partner on that record was Jane Birkin, acclaimed in France as a singer, an actress, a gap-toothed cultural ambassador nicknamed "L'Anglaise". Here she's best remembered for her part in Antonioni's Blow Up, romping in the buff with David Hemmings.

At that time, in the mid-Sixties, Birkin was married to Bond film score composer and notorious womaniser John Barry. A few years later, just out of her teens, she married Gainsbourg, who was on the rebound from Brigitte Bardot. It's hardly surprising that she seems to have spent most of her life in someone else's shadow. With her recent album Arabesque, Birkin is at last being accepted in Britain as an artist in her own right. Far from distancing herself from her beloved Serge, she is re-inventing his catalogue, adding a north African twist to songs that – in France at least – are virtually standards.

Thin as an asparagus spear, decked out in Juliette Greco beatnik black, the beatific Jane is quite shocked to see a packed Barbican – apparently no one at customs had recognised her as she came through with a French TV crew. "Gosh it's big here ... I'm so pleased to see you all." She says "gosh" a lot – a few decades in France have frozen her English so that her vocabulary has a very charming, Mallory Towers touch.

Early songs are solely accompanied by a pianist called Fred (or "Frrred", in the singer's pronunciation) who looks, rather inappropriately, like a middle-ranking snooker player. After a while the Algerian band appear to play Serge's "Elisa". They transform it from a circus tent pump-organ piece into a violin-led gipsy dirge, mournful and quite beautiful. It's followed by the only non-Gainsbourg song of the evening, a tribute written by "this beautiful girl called Zazie" with a chorus along the lines of "the songs of my dead love will never die". Jane sits, legs gawkily angling over the edge of the stage, almost in tears.

"And now, because the Barbican is elegant, we will try to do this elegantly." Everything is sung in Miss Birkin's posh whisper. Gainsbourg originally wanted Bardot to sing "Je T'aime..." (her husband unsurprisingly vetoed its release) – then he realised L'Anglaise's little voice could make the song doubly outrageous. He also got her to sing it in an uncomfortably high register, to make her sound even more like a pony-riding ingénue.

Now she's happy to accept her limitations. The vocals, like the arrangements, are gentle and warm, as if Gainsbourg's craft has been lovingly recreated in miniature. On "Couleur Café", maybe the first French hit to welcome a post-colonial populace, she softly encourages audience participation: "If you want to sing it too, sing it. But we have to sing it, you understand?" The audience bashfully demurs.

During an instrumental, Birkin attempts to leave the stage shouting "I'm off!" before realising she's run in the wrong direction. Like a startled deer, she doubles back across the stage, and re-emerges barefoot, a few minutes later, in a slinky red dress. She dances and grins to the nameless tune as if we're not there. The whole performance could not be more endearing. How odd that so many people in Britain believe her to be French. Edith Sitwell would have recognised Jane Birkin for what she is – a very English eccentric.