I’m afraid my knowledge of French film is very limited, but I thought Les Choristes (The Chorus in English) was pretty good. It’s about a teacher who ends up at a strict boarding school, and decides to change the attitude of his students by beginning a choir, despite the strong opposition of the director of the school.
Le Pianiste is another one. It’s about a Jewish pianist during WWII who is imprisoned in a concentration camp. Beyond that, I’m not to sure, as I never had the opportunity to finish it.
La Famille Bélier is about a girl who is the only member of her family that isn’t deaf, having to translate for them from sign language to French wherever they go, and who discovers that she is a talented singer.
There’s a list here of a number of French films (“the best [French] films of all time according to viewers”).
I suggest, unless your French is already pretty good, to watch movies with the English subtitles. This allows you to pick up on what they’re saying better, and to associate English words with the French ones. Otherwise, you’ll pick out the few words that you know, but you won’t learn many new ones. And, if you can, watch dubbed or subtitled movies that you’re already familiar with.
I’m afraid I can’t remember how straightforward the language was in a lot of the above. If you want to see a good movie, you might have to compromise on that… Watching dubbed movies you’ve seen already is your best bet to begin with. I also recommend that you watch a movie more than once. You’ll pick up more and more on subsequent viewings rather than having to start with a fresh story and maybe a different accent with another film.
Feel free to throw a PM my way if you want French help or practice.