Hi Alma,
Everything you want to do has been successfully done by others!
Your situation is a little different than mine, but not by much. Keeping that in mind, here are my thoughts.
1) you will not be working, so the long-term visa you are asking for is a visitor visa. As part of your application, you need to sign a letter stating that you will not work in France, and you need to provide proof that you have enough savings and/or income to live on. This should exceed 1500€ per month. You also need to show proof of the right kind of health insurance (minimum of emergency coverage and repatriation to the states if needed - eg world nomads has this, for up to one year). You tell them you want to live in France, not just stay for the one year (so that your visa is renewable). You only need to show all these proofs for one year. When your first year is up (actually, several months before), if you want to stay, you renew in France, and provide all the same type of documents that you provided for the first year. You will want to investigate this visa further, but those are the usual points of confusion.
2) after 5 years of continuous living in France, you can apply for citizenship. This process can take a couple of years. During all this time, you can still vacation outside of France and still be considered as "living continuously" in France - you need to be here >= 183 days each year, and file French taxes (and don't forget your USA taxes as well)
3) after 3 months of living in France, and after you have your OFII sticker/vignette (completing your first year visa status in France), you can apply via CPAM to get on the French health coverage system (via PUMA). It can take an unknown number of months to get processed. The cost is roughly 8% of your net income. But this is still getting worked out, so it's largely unknow for now. It covers roughly 70% of the "normal" costs, and 100% of chronic and emergency costs. You can buy a mutuelle (private insurance) to cover the rest - I don't have details on this. Costs here are much much less than in the states, so for us, our part is doable without the mutuelle.
4) Excellent that you are learning French ahead of time! You will not need it at the SF consulate, but after that, whoooee! Keep at it as much as possible!
Most people need to pass a test at A1 level when they arrive, then A2 level to renew, and B1 for citizenship. But if you're over 60, I think all of it is informal - no language level is required, but they do want you to know some French. And of course, if you don't know enough, you have to hire help, which makes everything more expensive.
5) If you do go for help, I have heard good things about pleasehelp.fr and parisunraveled.com - but investigate thoroughly. And consider contracting before applying for your visa, as that's a big part of what these companies do.
6) you don't mention this, but look into what you need to do about a driver's license. It is complicated!
Good luck!
Julie