OK, I'm late to plunge in here but hopefully not too late.
Ben is, I believe, half right. It's not possible for Alizée or her team to break into the U.S. market alone, there are things we need to do as well. But I also believe that she has not, in the past, tried, and if she doesn't try, then nothing we do will make any differnce. It's got to be a joint effort. So I'm going to start it this way.
1) Alizée, do you WANT to sell albums in America, and to perform in America? It would mean you would have to give up being anonymous when you visit this country. You could no longer go to New York or other parts of the U.S. and have no one (or almost no one) recognize you. You would have to be conscious of the public here as you are in France or Mexico. The commercial potential is of course huge. Is that worth it to you? If not, well, I guess we will simply have to accept that.
2) Don't be discouraged by the fact you don't sing (much) in English. The idea is not to be a mega-popstar-hit, but to reach a reasonable target audience.
3) The suggestions about venues for performance are good ones, but it seems to me the first thing is to make your music conveniently available in this country. It's often a challenge to buy your albums for Americans. Make that easier. Also, there has I believe been zero marketing effort in the past here. These two go together. It says to me that you (or your team, or your record company) don't expect to succeed here, or perhaps don't want to.
4) If you do perform in America on one of the shows, choose a song that can be enjoyed purely for the sound and the visual effect of your performance. Your lyrics are often poetic and powerful. Unfortunately, that part is going to be lost, until people are moved by you enough to learn French. But much of your music can be appreciated without knowing what the lyrics mean, and your performances -- when you're at your best -- are very engaging. That's what you'll have to depend on.
Despite this, I would recommend singing in French. You are at your best when you do.
5) When you do perform, do whatever it takes to boost your confidence. I know you get stage fright and are shy when breaking into a new venue, and America can be intimidating. But you are so lovely, so talented, and so sweet that you have nothing to fear. Let your light shine, and anyone who sees you will fall in love.
And that's about it, except that if you do this, do it because it's what you want. I once told someone who asked that I wanted for you to be happy and as successful as you want to be. Success has a price, as you know, and it's always a trade-off. If you do want to break into the U.S. market, we'll all help in any way we can. But if not, we'll survive, and still be able to hear your music and see you perform, wherever you go.