Yeah, why would Alizée want to be involved with the American music industry when the French music industry is working so well for her right now...
All kidding aside, (and I know I'm repeating myself again) but the music industry of the world is dominated by multinational corporations and I think there is less of a difference from country to country than people may think. I'm sure she feels safer and more comfortable in her own country (I know I would). But her career has been kept alive this last time around by the international music industry, namely Mexico. It's not something she can afford to be afraid of and ignore. Her continued success may indeed lie in the international realm. If she had been afraid of taking part in the Mexican music industry and decided not to go there, where would her career be now?
I would love nothing more than to see her successful in France again. But I think if an opportunity presents itself in the USA, she should at least consider it and not turn it down merely out of fear, (real or imagined).