You can try a place like last.fm or pandora. Last.fm's radio will allow you to play a "similar to Alizée" radio station that will play her occasionally as well as music deemed similar to hers. I use it relatively often. It doesn't have an extraordinary variety, but it plays good music.
Pandora.com is similar in that you enter a song and it plays music similar to it. When I used it in the past it had more variety than last.fm, but I stopped before it became a USA-only service. I don't know if it can play Alizée or even anything else French.
For a real radio station, try NRJ. I'm not familiar with it, but she revealed Mademoiselle Juliette at an NRJ studio. It sounds like a good place to try.
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