Yes, we are American citizens (and the wife gained EU citizenship thru ancestry). The only thing her EU citizenship made easier for us is that we were able to skip applying for a visa in advance of moving. We just had to show up and then apply for long term residency for me as the spouse of an EU citizen.

In France, residents (not just citizens) are able to apply for inclusion into the national healthcare system after being in the country for 90 days. Actually getting approved takes a few months, sometimes longer. Until then yes- we pay for everything out of pocket. We are also required to have a private insurance plan that includes remediation. These plans cover the basics excluding preexisting conditions. We bought one of the more expensive comprehensive policies and it cost us a little under $2700 for the year to cover both of us throughout Europe. There are, as stated elsewhere, much cheaper policies available but since my wife is T1D and we love to travel I didn’t want to take any chances with coverage.

We also had to prove sufficient funds- that was about 1600 euros per month, and either of our pensions cover that spread. Not going to lie, the pensions make this type of move much easier. I’m retired military and my souse retired early from a state university administration job. We don’t have “big money” as someone was suggesting, but we have enough to make this move successful.