I don't know why people classify it as a science fiction... it might have been at the time, but today the movie feels to me more like a surreal dream. I simply love it, I think it's one of Godard's greatest and most avantgard films.
It's more of what you would call a "soft science fiction" piece, like Philp K Dick's or George Orwell's novels (...juxtapose this film as a double feature with Truffaut's "Farenheit 451" and you've got a night), with the "science" being used more abtsractly to reflect humanity, as opposed to say the structural worlds of writers like Isaac Asimov (with rules and laws governing them)--with that I agree, it's definitely a surrealist film. ________ Yeah, I'm so bad, I kick my own ass twice a day... -Creeper the Hamburger Pimp
To me much of the film's genius is that it so seamlessly marries more than one category. I found it surreal AND sci-fi AND noir ...and lots of other things that we don't usually think of as movie genres, such as "absurdist" or "poetic" or "philosophical" or "ironic".
I wouldn't have thought this movie was really considered SF when it was made. Or particularly futuristic. It has all the appearance of a 1960s Paris setting. It has a pulp noir detective who was already out of contemporary at that time. I think it was just an enjoyably weird and illogical piece.