French cinema has a great past, it’s difficult to pick up only a few films !
First, I would love to talk about the silent period. A forgotten but essential name for me, Max Linder, who basically inspired Chaplin.
Georges Méliès and his famous Voyage dans la Lune. Napoléon by Abel Gance and L’Argent by Marcel L’Herbier are both stunning.
I would recommend Jean Renoir’s films, especially La Grande Illusion et La Règle du Jeu, more than movies, I think these two also tell something about French history and society. But any Renoir’s film is worth to be watched !
You could also try Marcel Carné, who directed the masterpiece Les Enfants du Paradis (with one of the most beautiful casts ever). Several of his other iconic films: Hôtel du Nord, Quai des Brumes, Drôle de Drame.
Julien Duviver directed the original Pépé le Moko with Jean Gabin (it would be remade in Hollywood with Charles Boyer, Algiers) and Un Carnet de Bal.
Max Ophüls’s films made in France: La Ronde, Le Plaisir, Madame de…, Lola Montès.
Robert Bresson’s films may left abashed but they are amazing. One of my personal favorites is Les Dames du Bois de Boulogne because of Maria Casarès’s flawless acting.
For comedy, Jacques Tati’s has a very poetic universe: Mon Oncle, Playtime, Les Vacances de Mr Hulot…
I’m sure I forgot many classics. I stopped with the late 50’s, I hope you don’t mind. I think those films can give a great start to discover french cinema ;-)
Have a nice day !