Gainsbourg was a very complex figure and writer-director Joann Sfar did a great job of trying to bring all those nuances to the screen. Originally a comic book writer, Joann Sfar did quite an amazing job bringing all sorts of different media to the screen. Puppets, cartoons, they all help bring Gainsbourg's character to life in a way that few biopics do.
With all of his famous relationships with gorgeous women, Vie Héroïque could easily have turned into a complete raunchfest, but luckily it doesn't (Serge was rather "pudique", after all). Brigitte, Jane and Bambou are put on little pedestals, just like Serge put them on pedestals. As far as I could tell, the whole film was very much in Serge's spirit; the puppets and cartoons would have been misplaced in any other biopic, but since Gainsbourg often talked of himself (or parts of his personality) in third person (Gainsbarre was his mischievous alter ego), it only helps to accentuate his character.
Sfar did a good job on the script, going from Gainsbourg just before the Second World War started to Gainsbourg at the end of the 1980s, handling all the major events, but I found it contained a few too many "warnings"; whenever something big was going to happen (writing for France Gall, writing 'Je T'Aime..', meeting Jane) the scene before holds a few too many hints as to what's going to happen. Maybe it's less annoying when you're not a complete nut and haven't read all kinds of biographies on him, though.
Eric Elmosnino is otherworldly as Serge; give that man a César already! To play someone as a stumbling 20-something, to an artist at the top of his game, to a man completely ravaged by alcohol and cigarettes without it ever becoming a caricature, it's amazing. When you watch interviews with Gainsbourg, you immediately notice his little physical quirks; the way he holds his head and the particular gestures he makes with his hands -- Elmosnino incorporates it all into his performance without it coming off unnatural.