I have been an International Chess Correspondence Federation (ICCF) delegate of a country for 20 years. So, the answer to your question is that you cannot transfer from France to USA in the ICCF without the approval of the French federation. But, in general federations would accept a transfer. You would have to contact the French Federation. However, the United States Chess Federation (USCF) accepts members even if they are not U.S. citizens. So, you can play in USCF tournaments. Note that USCF and US ICCF are not the same. USCF belongs to FIDE, but US ICCF belongs to ICCF. If you decide to do that, check that some U.S. tournaments do not allow chess engines, but others do because the U.S. is also a member of the ICCF. A good question is what is an official tournament? ICCF is the elder correspondence chess federation, but ICCF and FIDE are not 100% connected anymore. My suggestion would be that you play correspondence chess on lichess.org. Lichess do not allow the use of chess engines. Is it official? Why do you care about that? Lichess is the main chess server because it is 100% free. 250,000 members!!! For me that is an official system. Lechenicher Schach Server offers correspondence chess games without engines as well. Even they offer their website in French: https://www.chess-server.net/fr/ Lechenicher is also 100% free. However, be careful because they also have tournaments where the use of chess engines is allowed. Just register in the right tournament. My guess is that there are many other websites that offer correspondence chess without engines. Just do not limit yourself with the requirement of "official." At the end of the day, nobody cares about our chess rating except ourselves. Good luck with your chess journey! Hugs!
LSS now has a rating list for correspondence chess for players that do not use software programs (chess engines).
LSS is 100% free. An excellent server that I highly recommend.