France is one of the largest music markets, with a lot on offer. Mylène Farmer is a must! Rich, dark romanticism, and some of the most expensive (and amazing!) music videos ever produced worldwide! If you understand French, you'll love her lyrics, though the melodies themselves are evocative enough for you to get suckered in.
Another one to watch out for is Benjamin Biolay, a talented singer songwriter with an international flair. Vanessa Paradis, better know as Johnny Depp's beloved wife in anglo speaking territories, will also give you a run for your money.