I currently work in France where the law states that a 3 month notice must be given to the employer when leaving a position. I am currently trying to move to the USA, where employers are not very sympathetic with my situation, and I have an offer for a job starting in 6 to 8 weeks, ie before the end of my notice period. Does anybody have any advice about how to talk my current employer into letting me leave early?
This kind of problem should be the subject of polite and constructive negotiation.
Presumably your new US-based employer knows you are relocating from France, and presumably they offered you a job in the hopes that you will be with them for several years. The subject of the negotiation is a change of your start date at the new job of between four and six weeks. That is, objectively, not much time. So please don't exaggerate the importance of this. And please keep in mind that many companies do business around the world and are used to different employment laws in different countries.
I suggest you write to your new manager saying something like, "I need your help with something. Because of French employment law, my commitment to my present employer concludes three months after I give notice. If I am to meet my commitment, I need to start working for you on (whatever date). Is that possible? If not, what start date is possible? I personally place a high value on meeting my commitments, and I am grateful for any help you can offer me solving this problem."
Most employers like to work with people who try to meet their commitments. This sort of approach is likely to work. The manager will probably say "ok." If the manager comes back with a shorter time, he may have a good reason for it.
At any rate, then you can go to your present employer and respectfully say "what would it take for you to release me from my commitment on (date) before the three months have expired? Here is the reason for my request." They may say, "that will cost you 5000 euros." But they probably will say "finish certain work, and we will release you." They already know you're leaving.
Once you have had these conversations, you will understand your situation better.