Lots have been mentioned already, I would second Jean de Florette/Manon des sources, Caché (and anything by Michael Heneke), Amélie, Nikita, Le grand bleu, le bonheur est dans le pré, Ascenseur pour l’échafaud, La belle et la bête, Les diaboliques.
My favourite movie of all time is Les enfants du paradis, it’s long and old but absolutely beautiful and seminal. And makes you think about (I) how movies used to be made before CGI and (II) how little progress women have made in a century. The heroin is a kick ass goddess.
Anything with Fabrice Lucchini, he is hilarious and the most unlikely sex symbol.
Movies by Claude Lelouch (Les uns et les autres, Tout ça pour ça).
La Reine Margot (Isabelle Adjani)
L’été meurtrier (Adjani again)
La petite voleuse (Charlotte Gainsbourg), La Boum (Sophie Marceau), Les nuits Fauves (Cyril Collard and Romane Bohringer) - all three if you want to reimagine yourself as a French teenager in the 80s
Chacun cherche son chat
Au Petit Marguery
Also consider branching out to French Canadian movies (with subtitles if needed). Maybe start with Denys Arcand - Le déclin de l’empire américain, Jesus de Montréal and Xavier Dolan - Mommy, J’ai tué ma mère, Tom à la ferme.