As someone mentioned, you will need to check with your local French consulate for the relevant visa requirements. I will share with you what we went through to live in France for 18 months and, eventually, earned my carte sejour (residency permit to be renewed annually until after 5 years -- 3 for continuous living -- then you can get a 10 year residency visa).
- we already owned a maison secondaire in Languedoc which we used for holidays.
- we applied in Washington DC for a 6 month visa for French language immersion for our school age children; financial resources, health insurance, letter promising not to seek work or be employed, proof of residence in France, proof of school letter to accept children were needed. Consulate insisted that I accept additional documents to be filled out in France for long stay visa if we extend more than 6 months.
- Then (as someone mentioned, things may change, and this was in 2013), we arrived in France, completed the rest of the paperwork, sent this to Montpellier, to the prefecture (which will be in Toulouse moving forward because they combined the regions), and I received notice to get a health check up. Went to Montpellier, passed the health exam, received document to bring to our sous prefecture in Beziers.
- Another set of paperwork (birth certificates, marriage certificates, letter not to be employed, etc all translated in French with copies of original plus the original in case they ask to see --- the sous prefecture will tell you what you need to bring in their website) together with the Montpellier document will be required. Then the onsite meeting/interview (which is to go through the paperwork but not really in-depth interview) for the carte sejour. They gave me a recipesse while waiting for the carte sejour in case I leave the country and need to show proof of residence.
- you will receive notice to pick up the carte sejour and bring stamps (timbre) in lieu of cash or check payment. And you have to pick up the carte sejour personally.
- then you will have to renew this annually until you get a 10 year visa. Paperwork varies by the year and whoever is in charge of the sous prefecture.
Conversation with the sous prefecture and the prefecture is in French, BTW. Even if your French is not good, it is much appreciated and welcomed.
Also, you can be self employed but you will have to apply for the relevant paperwork in the sous prefecture which can take ages and cost euros. I know retired Americans have done this so they can pay into the system and receive a carte vitale. You cannot apply for carte vitale with an annual or 10 year carte sejour as an American citizen. Like the US, you have to pay into the system to enjoy the benefits. However, the out of pocket doctor visits, ER visits, diagnostics and preventive treatment, I think, are still cheaper than the co-pays in the US.
You can email me at email@example.com for more info.