Louis Malle has been mentioned. My personal favourite of his is Le souffle au coeur (Murmur of the Heart).
Have a look at Ascenseur pour l’échafaud, (Elevator to the Gallows), also by Louis Malle. Great movie from the film noir era, with an awesome soundtrack done by Miles Davis.
came here to suggest this; many years ago I was wandering the rows of the local blockbuster and the clerk asked if he could help me find anything. I jokingly responded with, “recommend something that will make me ashamed to be human” and he suggested this title without even skipping a beat. I have no idea why I responded the way I did, nor why he made the recommendation based on my response, but I’m glad it went down the way it did - very enjoyable movie.
Oh, there’s also District B13. I wouldn’t necessarily say it was “very good”, but it was a decent action flick with some great parkour sequences.
If you want some slapstick time travel comedy, Les Visiteurs fits the bill.
36 Quai des Orfèvres - an excellent crime story about two detectives competing for a promotion.
Un héros très discret - a dark comedy about a young man who pretends to be a member of the French Resistance.
Another vote for both Delicatessen and Rififi - both excellent films.
Diva is a thriller that I’d definitely reco (it has a 96 rating on Rottn Tomatoes).
Rules of the Game is a must see - directed by Jean Renoir, and often ranked in the top 10 of all movies.
My personal favorite, though, is Shoot the Piano Player. Directed by Francois Truffaut, starring Charles Aznvour; it contains elements of melodrama, noir, and slapstick. Highly recommend.
I should have mentioned Army of Shadows (L’armée des ombres) in my earlier post. It is a superlative, absolutely gripping film about the French Resistance in WWII. Outstanding in every way. And, oh, so tragic.
I knew a lot of the movies suggested would be posted here, but I figured this one would have been overlooked; it’s a terrific fun cop-buddy-father-daughter movie but unless your a big Luc Besson fan (points to self), it likely was under your radar.
Not much dialogue, but Banliue 13 (known in the States as District B13) is one of the best buddy cop/chase movies ever. It’s sequel was just okay, but B13 totally fucking rocks; it features one of the best opening sequences ever.
I already mentioned District B13, but yeah. It makes you want to do parkour, until you step back and realize: If I tried to do parkour, I’d break multiple bones before I even knew what the crap I was doing. 
La Haine is one of the best movies of the last 20 years nobody ever talks about. It actually was only available as a bootleg until 2007. Follows 24 hours in the lives of three 20 somethings in a housing project outside Paris during the riots over police brutality and is vaguely based on real events. Although it’s set up as a cinema verite style documentary, it actually has breathtaking cinematography, even by French black and white film standards.
Another scene
Opening scene
I’m still here, lurking. Great suggestions and so many. Thanks.
I’ve got this whole thread on “save”
Glad to hear it 
If you get round to watching any, it’d be interesting to hear what you think.
I can’t believe your name didn’t register with me when I pointed out Army of Shadows (L’armée des OMBREs) in my earlier post. So, I’ll use my cluelessness to say again: it is a superlative, absolutely gripping film about the French Resistance in WWII. Outstanding in every way. And, oh, so tragic.
I don’t think it’s a movie ‘nobody’ ever talks about. Wikisays it ranked #32 in an Empire’s magazine list of 100 best Movies of World Cinema, and that it did well in the box office. I remember it being widely available in Europe. You may have had this in mind, but it’s worth pointing it out that the movie came out a full decade before the 2005 riots in Paris (not sure if that’s what you meant by ‘the riots over police brutality’, but those are surely the riots that went the furthest and gained the most attention). Of course, many of the themes touched upon in the movie (housing projects, police brutality, multicultural society, etc.) intersect with key factors in the 2005 riots.
I’m hoping soon to get my paws on a copy of Martin Villeneuve’s SF work, Mars et Avril. It’s available on DVD and the iTunes Store here in Canada; I just need to get paid. When I was in Quebec, I walked into an Archambeault store and had a copy in my hand and didn’t have the money to buy it.
Don’t miss Martin’s TED talk: http://www.ted.com/talks/martin_villeneuve_how_i_made_an_impossible_film.html
Another vote for Amélie.
C’était un rendez-vous finally got a proper transfer and DVD release after being only on bootlegs for years, but it probably wouldn’t be all that helpful for someone wanting to practice his French language skills.
La haine was inspired by earlier riots. It certainly isn’t an obscure movie, at least not in the francophone world. I saw it three or four times, and not necessarily because I liked it that much, it just happened to get played everywhere. It was certified cult movie before it even came out – there was quite a lot of hype around it. That being said, it’s really not a good movie if you want to learn French! I know otherwise perfectly fluent speakers who could barely understand a word that was said. The dialogue is mostly improvised and entirely in street slang.
No love for My Father’s Glory (La Gloire de Mon Pere) and its sequel My Mother’s Castle (Le Chateau de Ma Mere)?
Wonderful films about a boy vacationing in Provence around 1910 and exploring the countryside.
Jean-Pierre Jeunet’s films are great if you like his style. Amelie, Delicatessen, and Cite des Enfants Perdus are his classics, although his later films are not bad.
(Except for Alien Resurrection. That one’s pretty bad.)