Hey man,
Feel free to PM me if you want to talk through some details. I'm also French originally from Paris/Versailles area, currently residing in Atlanta with my wife who is American.
I got my EASA Private in France and recently got my FAA Instrument and Commercial. Your hours in France or wherever you fly in Europe will absolutely count. Take advantage of the time you have now to knock out your Private and build some time. Just keep in mind that when you move to the US, you will find that things are done a bit differently so you will most likely need to do some more time building to feel comfortable, depending on how current and proficient you are.