I'm not sure what you mean by direct link, if you just want to watch videos of her performances you can browse the
AAm video section. If you want to download videos of her performances, there is this thread on AF with download links to pretty much every video (including performances) that exists of Alizée during the Gourmandises/MCE era.
http://www.alizee-forum.com/showthre...liz%E9e-Videos
I realize that those are quite a lot videos, so I'll take the liberty to recommend some videos of her performances that I consider must-have.
Alizée - 2001-04-30 - Performance - Moi... Lolita - Live In Amsterdam.mpeg - 179.7 MB
http://www.sendspace.com/file/rj67s5
(Hands down the best performance of Moi... Lolita)
Alizée - 2003-03-03 - Performance & Interview - J'en Ai Marre - Pour Laurette - HQ.vob - 372.5 MB
http://www.megaupload.com/?d=UMU3DE54
(I discovered Alizée through this video)
Alizée - 2003-07-04 - Performance - J'ai Pas Vingt Ans - Les 100 Ans Du Tour De France.mpg - 168.1 MB
http://www.sendspace.com/file/od3uxc
(Actually, I'm not sure which of her JPVA performances is the best, so I went with this one)
Alizée - 2003-03-15 - Performance & Interview - Ella, Elle L'a - France Gall Cover Chanson N°1 - FR2 - HQ.m2v - 209.4 MB
http://www.sendspace.com/file/6d2wmn
(She looks so beautiful in this performance, I don't know why, but there's just something special about it)
Alizée - 2003-06-08 - Performance - La Isla Bonita - Chanson N°1 (By R. Spark.) - HQ.mpg - 135.2 MB
http://www.sendspace.com/file/9o3xz5
(Enough said)
Alizée - 2003-07-04 - Performance - I'm Fed Up - Top Of The Pops - RTL (dvdr-2003) - HQ.m2v - 109.9 MB
http://www.sendspace.com/file/p0wnou
(Her only performance of I'm Fed Up)