> The "Social security" pays around of 10% of most usual costs, the mutual fund pays the rest...

What? The basic insurance scheme pays at least 60% of a set of reasonable, negotiated fees and the "mutuelle" covers the rest. There are a few corner cases (complicated dental work, optics) but these are being addressed. Usually the out-of-pocket expense is minimal to nil (a "forfait moderateur" of around 1 euro per doctor's appointment for instance)