EmilyA

I think as the OP is female she will get to retirement age before the 2 years for S1/E106 + five years residence, even given the new retirement ages. I also gather that there is now doubt about whether some private insurances are acceptable or not; I think as ever it is likely to be down to interpretation by local CPAMs, because nobody really knows.
We were unlucky because we have been here since 2005, but our E106 ran out before the French government changed its mind in early 2008 and said we could be in the CMU after all. We opened and ran a business, got health cover that way for 3 years and now have S1s from UK state pensions via our business caisse. Running the business was a nightmare of bureacracy and we paid huge amounts in cotisations, but we gained a lot from the experience!

Im_and_Er

There is a lot of useful and authoritative advice on health matters on this site including the legislation outlining what constitutes private insurance:

http://www.frenchhealthissues.eu

The site founders were responsible for the campaign and lobbying which resulted in the partial climb down by the French.