If you send money from a typical French bank to a US bank, they're likely to take some fees and/or give an exchange rate worse than the interbank exchange rate.
Revolut uses the interbank exchange rate for EUR <-> USD on weekdays (Mon-Fri UTC) and don't have any fee, so that's the cheapest option I am aware of. They do have a limit of 6,000 EUR / month (reset on the 12th midnight CET of each month), above which they'll take a 0.5% conversion fee (unless you purchase the premium/metal accounts, in which case there is no limit).
Other options: N26 (I haven't tried it) and TransferWise (more expensive than Revolut: they charge a 0.5% fee on the conversion).
Fee comparison from https://www.starlingbank.com/send-money-abroad (Revolut is the best in the benchmark even though it was done by a competitor, starlingbank):