Perhaps a silly question, but did you see 'useful links' at the top of the page, between Amazon and Services? There is Health several down the list. Here is the direct link: http://www.survivefrance.com/page/health
Em has given you more or less the answer you need but there is always more and also those useful links and any comments or advice that go up on them are part of work permanently in progress.
We are lucky, because one of one daughter's friends is an insurance agent. We already had insurance through him before the girls knew each other, but parents of school friends tend to get to know each other and become part of the same social group, which in this case was our good fortune. He knows not only the workings of complementary and private health as well as all other insurance cover but also how the state systems function. Being a parent with that background he can unwrap a great deal more. Now, it might take a bit of looking, but given that this agent exists logic says that there must be plenty more like him. Finding them is another matter. We hit luck almost too easily. However, it does suggest that getting to know your insurance agent and finding out what he/she knows might help a bit/lot depending on your luck. Try that since there is nothing to lose.
We have never had any problems whatsoever but at the same time have learned that no two offices or sections of the health system (and other areas) seem to be interconnected, share transferable knowledge or whatsoever. Sometimes it is hard work. That is one of the things the useful links pages are for and why I am suggesting finding somebody from outside the state system who knows. Best of luck with it whatever happens.