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MLabinov wrote:

Is there any way to buy property in France and obtain the health coverage ?

Go to an estate agent and any of the private heath plan vendors.

I am talking about a connection between property ownership and residence to  get access to national health  coverage..

I understand what you are trying to do. Fact is that the French health coverage is so far superior to the US that I am surprised more people are not trying to do the same. A call to your nearest French consulate should get you an answer.

I live in California no where near a French consulate.  If you call you are told that any conversation must be conducted in person by appointment only.

Hi, then I see two options for you:
1. You take a trip to your closest consulate. After all, if this project is important to you, it will take some work.
2. You do searches on the internet to get an answer to your question.

Best wishes to you.

The two are not connected.
Once you have established a residence in France (lived here 3 months), and have your visa with vignette, you apply at CPAM for your Carte Vitale. It can take an unknown number of months to process.
Step one is to get a visa - you are comparatively close to your French consulate in California. You cannot just drop by anyway; you need an appointment.