The most that would happen would be for Coldplay to agree they infringed and then pay Mylene (not ALizée). I doubt Mylene would sue. Most likely the record companies would simply deal with it.
All Alizée can hope to get out of it is a few headlines - or perhaps many if the press really runs with it. As we all know, headlines are essentially always good publicity.
Let's hope the make a BIG deal out of it.