If I was going to send something myself, I'd probably try sending it via Alizée's label, Sony Music France.
http://www.sonymusic.fr/contact/
Alizée c/o Jive/Epic
Sony Music Entertainment France
52/54 rue de Châteaudun
75342 Paris Cedex 09
FRANCE
You'll have to fill out a customs form with your package, they can help you with that at the post office.
But I have a feeling that she wouldn't put a non-commercially made DVD into her player or computer.
Your best bet might be to post it on YouTube and then Tweet
on Twitter about it.
There are probably some other, better methods but I am not aware of any.
Good luck!