It would be nice to know what the comments were that prompted Alizée to respond in such a manner. It didn't appear to be a direct reply to any particular tweet. I suppose it's possible she was responding to things being said in places other than Twitter.
On one fan site, a few people have said they preferred it when she didn't communicate to fans because they liked the mystery and suspense. A few others have said that they wish she would use Twitter to update us on the progress of her album rather than her latest clothing purchase. But it seems to me that the majority of fans are very happy with the way she is communicating through Twitter.
There will always be critics, regardless of what she does. So she might as well do what she wants to do and have fun with it.