John,
You and I are in much of the same boat as to finding ourselves in a quagmire of information. But, we are smart people and can get through this, lol. Unlike you, I am retiring with my husband and moving permanently to Bordeaux, so my situation is a little different, but not that much in that we both still have to fulfill the requirements set forth by the French Consulate in Miami. I will share some information that I have learned and some frustrations, so if anyone can shed some light please do.
As you mentioned, you won't have to pay taxes in France since you are 1) not earning money there
2) pay the lesser rate of the two countries
In order to get approved for the Long Term Stay Visa, you do however have to provide a residence in France. I don't know how this will work since you will be mobile, but perhaps there is a Mobile home Park that can provide you with an address, but you will have to show a rental agreement, and maybe a utility bill. Certainly you aren't the first, so look for a Park that you could lease a space for 6 months or so, and ask them to provide proof of the agreement.
You must also have Global Insurance that must meet minimum standards, and provide proof of this to the consulate as well. I have found several companies that I am waiting for quotes on, but since my husband and I are retiring early, we are still paying for our premiums here which are about $1,800.00 per MONTH, and even the best Global plans are much cheaper, so that is a great thing .
After getting to France, it is very possible that you will have to have a French bank account, definitely for us as we are setting up residence.
This however has been the source of much headache. The US has made the banking laws very complex, and France to be quite frank, doesn't like to have to do all the extra paperwork required, which is odd since they seem to love paperwork! I went to get a real estate agent who said I had to have an account first, then went to the bank which said that I needed an address first. Now I have to find an Airbnb for several months to provide the Consulate and the bank.
I am sure you wont have a problem with providing proof of your assets, but just remember that they require a minimum amount, to guarantee you will be covered while you are there not working. So, from what I understand, it is your rent (which with you is ambiguous ) plus around 800 euros per month. If you are staying for 12 months, and your rent is 1000 euros per month, plus the 800 for expenses they require, you need 21,600 in funds, again not a problem for you but others should be advised. I am going to include a few links that have some great info, and I hope that I have helped a little. Moving from Fort Lauderdale to Bordeaux is providing to be a bit of a challenge, but once you have been to Bordeaux, you never want to leave! It is awesome and I hope you get a chance to stop there on your travels.
globalinsurancenet.com
theamericaninparis.com
americansinfrance.net
the local.fr
takelessons.com
jeantaquet.com
Good luck!
Kelly