I add a +1 to Stephanie's comment for "9 mois ferme"!

Other famous French movies are "Intouchables" (how a disadvantaged black buy gets to know a kind of rich guy, but who is tetrapleagic and how they learn from each other and become good friends through their differences) and "Bienvenue chez les chtis" (maybe more difficult, because it is about cultural differences and prejudices between north and south of France, so the accents of the characters may be hard to understand sometimes). 

I like French romantic comedies (so light comedy with some social/psychological background). I can recommend you:
"Fauteuils d'orchestre" (the story happens in a quarter of Paris. Some people from different social classes meet: a waitress, an actress, a concert pianist and an old man who sells every art pieces he collected during his life in an auction between others).
"Je vous trouve très beau" : a widowed farmer searches a new wife, not because he is romantic, but because he needs someone to clean the house. He goes in Rumania to pick a wife... but the girl he chooses change his life more than he thought it possible.
"Le prénom" : It's a family dinner, one guy tells his family in law that he wants to name his future child "Adolphe"... the family is chocked because it sounds like "Adolf Hitler" and so it's very badly connoted... and it brings the family in crisis: every unsaid things are revealed.
"Ensemble c'est tout" : Three roomates + one^^ An anorexic girl, a young man from the nobility who stammers and a cook take the grandmother of the cook guy with them when she is unable to live alone.
"Qu'est-ce qu'on a fait au bon dieu" : A couple has 4 daughters. They are good catholics. But the drama of their life is that their three older aughters have married respectively a muslim, a jew and a chinese... They hope their last daughter won't disappoint them again... her lover is catholic! but he is black...

I recently saw the French film "La French".  The American title was "The Connection", and it was about the real event of an international drug ring based in Marseille called The French Connection.  This is a brand new film (not the old one of similar title) with Jean Dujardin. It was amazing, exciting and very well made. 

I also saw a comedy called "9 mois ferme" (American title "9 Month Stretch"), with Albert Dupontel. It was great too!  It was a very funny story and at the end I really started to like the characters.