Anyway, Kate had some good recommendations. Also, you should try watching some Haneke movies (Kate mentioned Caché), so Amour seems obvious right now. Intouchables is another pretty new movie that everyone loves. Le scaphandre et le papillon and Le fabuleux destin d'Amélie Poulain are also must sees.
If you want to dig into intellectual stuff, then Jean-Luc Godard, François Truffaut, Robert Bresson and Jean Renoir are the way to go, but most people usually find those directors boring.