Like you, I am a retired federal worker who has been living in France with my wife for almost 4 years.
Another reply here informed you:
"Because you will not be allowed to work legally in France, you will have to prove that you can support yourselves during the given time frame - the amount you're required to keep in a French bank is equal to or more than twice the minimum-wage level in France (SMIC) for each person.Â
If this amount isn't available, you'll have to find someone to sponsor your needs while in France, make sure the money is in the bank, and who will have a notarized affidavit written and translated."
While you will have to provide proof of your resources, I have never been required to maintain a French bank account. This might apply to someone else but, as I say, this was not a requirement for us. You will not need a sponsor. This writer might be confusing this with a requirement that you provide documentation of a certain minimum amount of month income which should be no problem.
"Your insurance must also cover all repatriation costs. If it doesn't, find out if it can be added, or look for additional insurance."
I have no idea where this comes from but it has never been required of us.
We lived in Florida and the closest consulate was in Miami. There is also a link on the website of the French Embassy in Washington that can direct you to the proper forms.
It is correct that you might have trouble opening a bank account and this is all due to a law passed a few years ago known as FATCA. It has been created problems for a lot of Americans living overseas so it might be a good idea to familiarize yourself with this. We bank with Barclays but have had some other issues with US based banks due to this. I will mention this, though, if you have funds in the TSP, they will not be affected by this. I had a TSP account which I foolishly rolled into an IRA. After FATCA, I was forced to close my IRA and all other investment accounts I held with USAA and had a terrible time trying to find anyone to take us. The Patriot Act also has something to do with this.
Please don't be unduly alarmed by this but it is something you need to be aware of.
On the bright side, the visa process wasn't any worse than any DMV experience I've ever had and because you are Americans you will be welcome here. Err on the the side of too much documentation. If you're going to be living in Paris, you might not have too much trouble if you don't speak French. I could not speak French before we came here and it is a struggle. My wife speaks it well but as you know, the language of bureaucracy can be difficult.
The first visa will come from the immigration office but is easily renewed each year at the local prefecture.
Good luck.