By one of the co-directors of La Cité des enfants perdus / The City of Lost Children (Jean-Pierre Jeunet):
Le Fabuleux destin d'Amélie Poulain (also known as Amélie). Truly an adventure. : )

Nikita (also known as La Femme Nikita) is also a good introductory film.

I would recommend others, but, they might be a bit overwhelming for those not well-acquainted with French cinema.

Intouchables is always a great "light hearted" watch.

Loaded Weapon 1, it's still funny.

Dawn of the Planet of the Apes. Was quite better than I expected since the first movie is kinda only okay-ish.

I saw Amélie at the cinema. It was fun and well made, though I did not think of it as extraordinary. I ave also seen Vidoq and some of the Astérix movies. I have not seen Nikita, though I have heard of it.

Sadly, most of the French movies I hear about are light comedies, and they don't look too clever or interesting to me. I could be wrong, though.
Thanks for helping.

If you like animated films I would recommend April and the Extraordinary World. I'm a sucker for 2D animation which barely gets feature films these days, and it's a fun, original steampunk adventure.

Montauk Chronicles.