For example, Nikos Aliagas at one point asks:
-D'ou vient cette connaissance de la langue française? - Literally, "from where comes this knowledge of the French language?", a delightfully French way of asking "how come you speak French?"
Bradley Cooper obviously speaks French really well. He uses quite a lot of modern words and phrases in his French. Here are a few things that I noticed:
Tu connais le mec? - Do you know the guy?
Ouais - instead of oui. I.e 'yeah' instead of 'yes'. Not exactly revolutionary, but I think I'm still saying 'oui' most of the time.
C'est hyper facile de jouer avec quelqu'un qui joue pas - hyper instead of très
Finally, I absolutely have to mention that the French title for The Hangover seems to be Le Very Bad Trip! Brilliant!
Bonus bit of vocab: the French term for stag-do is enterrement de vie de garçon (literally, 'burial of the life of the boy'). Likewise, a hen-do is enterrement de vie de jeune fille.