You can find French music here :
http://www.deezer.com/fr/
You must to register, but it's totally free.
Well, I can advice you to listen Serge Gainsbourg, Vanessa Paradis, Mylène Farmer,the first album of Nolwenn Leroy, the first album of Carla Bruni, Milchel Polnareff, and so on... You can find all the Alizée's songs too.