I went through some of Alizee's interviews that she did in 2008 that I have in document form. I wanted to see if she had said something in depth about the video in an interview. I came up empty except for a excerpt where she is answering a question about clothes:
"I'm a big fan of clothes. I spend all my money on clothes, you could say! In fact, I asked myself the question of if in the photos, in the music videos, I would again play a role as far as my clothes, or if I would wear exactly the clothes I like? I wanted to wear something new, I really want in the videos and photos to wear things I love, but which I couldn’t wear in my daily life, in the street.… I have a period corset in the video, a real corset, wasp-waisted, like that. But yeah, it’s a bit of all that. Also, I try to me inject a little bit of current fashion, without making it too distinctly dated – things that will not have become unfashionable in 10 years, much less in 6 months."
I think some of the words did not translate very well but it is still understandable.
Juliet is a fictional character from the 14th century. As Alizee says, in her videos she wanted to wear things she couldn't wear in real life, so she or the producer fit a corset on her. Maybe this is a vision they had of Juliet. I had to look it up, but French corsets were not invented until the 16th century. The fashion is off by a few hundred years.
There is probably some symbolism in the video but I'm not sure about a deep meaning. Some things seem a little random. The girls in the bathtub is something Mylene did in her Libertine video. I think I remember reading more about this video some time ago. I will try to keep searching when I have more time.