The thing is,in my opinion, you can't have a balanced insurance system with health costs as high as the US ones. So you would have to force everyone to reduce their rates, and thus decrease the cash generated by this economy ( and thus less R&D)
French doctor rates are fixed (unless they decide to have their fees not rembursed by the NHS), and they are orders of magnitude lower than the US ones ( remove one and sometimes two zeros for exam fees).
And even with thoses restictions, french NHS is struggling economicaly.