Alizée has a very unique cute voice that fits well with her personality !! That said she doesn't have a natural singing voice, like others have said already her singing requires a little more training and practice. A good sample of natural singing ability could be heard in the voices of Natasha St. Pier, Jenifer Bartoli, Nolwenn Leroy, Laura Pausini, etc. It's one thing to have a passion for singing, and another to sing with passion. If you can feel the passion in their singing, then you know they have a good singing voice...
That said, this doesn't guaranty that everyone will like them because of their great singing voice, there's other factors involved in liking an artist, like the style of music they play, the artist's appearance and the way they portray themselves, etc. Everyone has their own criteria of this...