Perhaps. I know at least three retirees doing that (spending winters with their family abroad), and apparently there's a term for it in the UK ("mouseholing"), but I can't find any statistics.

That's seasonal living between two places (e.g. Snow Birds). Presumably there is already a workable solution for those folks. Parent was talking about people who randomly move country to country.

I am Parent, and I wasn't, even if I didn't explain myself clearly :)

Is there a workable solution? I don't have any experience with the French system, but between the two EU countries I know, there's no good solution, or at least none was offered by doctors on either side.

I believe that in the US/Canada the solution is for the patient to carry a backpack full of medical records. Honestly though based on my experience with the medical system in several countries, and talking to medical provider friends, I'm not sure records, apart from very recent ones, achieve much anyway. e.g. Dr B won't trust that Dr A made the right diagnosis or that an old test result is to be trusted, and so on.

Personal example : I migrated (legally) from the UK to the USA 20 years ago. USA wants you to prove that you have vaccinations. However they don't actually take UK medical records as proof. Easier to just make everyone have the vaccinations again!