The French medical system is a 'pay as you go' system where the social security authorities reimburse people part of the costs (usually to a ceiling). Companies usually put in place an insurance plan (une mutuelle) that reimburses some (not always all) of the balance once the state has paid its share - insurance costs are usually split 50/50 between company and employee. Consequently for obvious structural reasons, the UK type of cashback system does not fit into this model.
Have you asked your current supplier if they can offet you a french-type cover?

Your options are currently fewer than Ray's answer suggests because every position in France is covered by a 'convention collectif' (CC), either a specific national branch agreement or the default general agreement that specifies minimum employer obligations. If you wait a few months, one of the reforms that the new president proposes (and is working on) is to give local company-based agreements priority over the applicable CC.

In reply to Ray:

Thanks Ray, much appreciated.

In reply to Nicola:

Thanks David, much appreciated.