hana_sanctuary, I'll upload some my favorite French songs later.
for Live Webradio, I recommend
Frequence 3. I started listen to this webradio since this January, and Frequence3 is not just a French music radio, they also plays many great songs from other countries (USA, UK, German music.) so that's why I love this webradio. (plus, they'll show every tracks, so if you like the song they just played, you could check it on the site.)
EDIT: hey guys, here are some of my favorite French tracks. five songs included.
Kyo - Ce Soir [Tonight] (soft rock ballad)
Jonatan Cerrada - Mon Paradis [My Paradise] (totally pop, the theme song of the animation "Robots" in France)
Larent Voulzy - Je suis venu pour elle [I Came For Her] (released in 2002, I think it's the best of all. a touching ballad)
Calogero - Face à la mer [Watch The Sea] (a mix of rap and rock. I think Calogero is a legend, and he's talented too.)
Raphaël - Les Petits Bateaux [Those Small Boats] (it sounds disconsolate to me, I felt sad whenever I hear this song.)
Download
here.