Indeed we are indeed using the french Social Security system and paying the Social Contributions for that right. When we first moved to France we took out full private health insurance thru a group called Mondassur - ASFE. Their cover was excellent and covered 90-100% of our costs. They were not cheap, but certainly far from the most expensive. The benefit to us was that we were covered for our pre-existing conditions (other companies would not cover). After our first 18 months, the laws changed in France to allow “anyone” who can prove that they have lived in France for a minimum of 3 months could apply for the Carte Vitale (Medicare). We received our cards in 2015 and it was only this year that they have started to charge us for the Social Contributions on our pension income. The social charge on pension income is only 6.90% but it is 17.2% on investment income. We find that currently we are paying about half of the cost of private health cover and about the same as we were paying for “Hospital Only” private cover in Australia. With the french system, we are covered for all medical costs (radiology and pathology included) as well as proportionate amount for dental and optometrist. Of course you can (we do) also top up with a “Mutuelle” so that you are covered for almost 100%, with some exceptions. It is indeed a good system.
To self insure is not regarded as possible by the french as under your visa application you will need to have health cover and if you renew your Carte de Sejour they will want to see evidence of your cover each time.
Hope this helps…probably best to get into the french system once you have been here for at least 3 months…it can take 3 months or so to get the carte vitale these days, so you would still need cover for the first year.