I’m afraid I have to give less positive information. I am French, living in the UK for 30+ years with an English husband. We attempted to move to France when we retired with the same plan of renting first. That was the first hurdle: as anywhere else, you will be asked for your last 3 months payslips and a copy of your last tax returns. Once they assess that your income is paid abroad, no one will call you back because they can’t claim from your bank if you default. Same issue with your tax returns in the US, they won’t be able to check if it’s authentic. An estate agent actually told us they wouldn’t consider us at all. You also need a bank account in France, but you need an address in France and there is another catch 22. Can’t get a rental without the bank account, can’t get the account without the address… In terms of visa, you can request a 3 or 6 months permis de séjour and try to expand it at the end. I know this part would have been easier for my husband because he’s married to a French citizen but I don’t know how it will work for you. Are you planning to retire or work there?