I think the song "Coeur deja pris" ("Heart belongs to another") from her second album, "Mes Courants Électriques," is one of her most beautiful songs. I especially like the chorus:
"Keep me close though you love another
Keep me close, can't blame me altogether
Then if I see it's my choice:
Your heart's not free ...for me, so
I believe, sometimes love plays a game with me.
Then keep me close
It was said, I know: your heart's not free, just
Keep me close
If it must be this way."
Alizée never performed this song live, but here is a nice video that someone put together: