Try Élodie Frégé.
La ceinture is absolutely lovely.
If you like Björk, you'll probably love Camille. She's the French Björk, and she's so awesome.
Although she doesn't sing fully in French (in fact, only a small amount of her songs are sung in French), Madeleine Peyroux sings some great light jazz music.
I liked Slaï's
La Dernière Danse. Very charming.
