RMJ, in an interview, Alizée pretty heavily put down singing in a language one doesn't understand, and said she was taking English lessons so she would be able to sing in English. I think we can depend on it that she understands the lyrics of any song she sings in English.
If she's like most people, she can probably understand more spoken or written English than she can speak. I'm definitely that way with French. I'm getting to the point where I can often follow Alizée's French lyrics and interviews, but I can't trust myself yet to put words together in French from a cold start.
Her English is no doubt better than my French. How much better is guesswork.