I see some incorrect information (or at least, information that is inconsistent with my experience living in France), so I thought I'd add to the discussion.
Also required by the OFII will be an official chest Xray. This is done a special immigration medical facility.
This is inconsistent with our experience. Yes, we had to have a chest x-ray done in France as part of the OFII process, at nominal cost, but it was done at a normal medical imagining facility, not a "special immigration medical facility."
Stephen also says that you can't get a Carte Vitale under a long-term visa. When you can get it, I don't know. But I've often heard the three-month thing, so who really knows?
One has to be careful with information, paying attention that you access current information. It's easy to find references on the internet or in published books saying one cannot get French health coverage under this or that kind of visa, if you're retired with no income other than a pension, and so forth. That's outdated information.
In January 2016, France implemented a new law called protection universelle maladie, often abbreviated as PUMa or PUMA. You can read about it here (pick any postal code when prompted -- it doesn't matter for this purpose). If you don't read French, use an online translator such as Google Translate, Bing Translator, or DeepL.
In short, the law that went into effect in 2016 assures universal health coverage to all legal residents of France after 3 months of residency (though the process of applying and getting approval, along with your Carte Vitale, takes another 3 to 6 months beyond that, so the practical effect is you'll probably need the better part of the your first year as a French resident to get the process set up).
To immigrate to France, you need to show that you have health insurance, including repatriation coverage, for one year, unless you have coverage through your employer in France. Under PUMA, that means you won't need that full year of coverage, but that's the requirement.
In addition to the universal coverage provided by the government, most people buy heavily regulated supplemental insurance (referred to as a mutuelle) to cover things the universal coverage doesn't. I have read the cost of a mutuelle can range from about 75€ to 150€ per person per month, depending on the company and options selected. We pay 94€ per person per month for my wife and me.
For many retirees, it's a pretty good deal now that they're eligible for health coverage under PUMA. That's because the 8 percent cotisation (social security tax) that is deducted from French workers' earnings to pay for health coverage is only owed if one has annual income from wages or capital gains above a certain threshold (about 4,000€/year for a single person or 10,000€ for a married couple).
But your pension or annual IRA/401(k) withdrawals would be higher than that -- won't you have to pay the 8 percent on that?
Nope. France doesn't count pensions or IRA/401(k) withdrawals as income. They're considered pensions that have to be reported to the tax authorities but no French tax is owed on them. For a retiree who isn't working, he or she would have to have capital gains, such as interest income above the thresholds cited above, to owe a cotisation for health coverage.
You'll still owe income tax to the IRS, of course, but that's the way the tax treaty between the U.S. and France is designed. So - an American retiree in France gets the high service benefits of a high tax nation like France but has to pay the relatively low tax rate of a low-service nation -- the U.S.