I remember thinking the same thing watching that performance the first time. In fact, I had thought maybe some singing like that would make it onto '5' which wouldn't be released for a few more months. Well, she chose to make that album the way she wanted, not the way I wanted. (Of course I've come to love it.)
And then I also remember hearing about it not being live singing (of course the show was pre-recorded) and I wondered about that, though I'll never be convinced it wasn't. I just watched the HD recordings from that song and also the duet she did for
Americain and I still can't say if it's playback or not. I'm no expert of course. During the duet towards the end it looks like Chimene Badi started to sing a line that Alizée was singing, and it could be indicative of playback. I don't know. Either way she has a great sound on that show and I wouldn't mind hearing more from her like that.
Here is an audience recording from the duet, it only covers part of the song. (Not the part I mentioned)
And here is audio from the whole song. It won't show the part I mentioned above though, as it was a visual thing. (The audience vid starts at around :17 in this one.)