I would not go thinking an E111 will cover you! Mr MC got stretched off Le Pleney by trumptons in 2009, speaking no French he ended up in a private French hospital having the top of his knee (tibial plateau) screwed back on ... and 5 days in a nice hospital, where he got proper 3 course meals. We forked out the minimum upfront .. which was still probably £1000, and that was what the E111 covered us with!!!
2007 we also claimed from insurance as he tore ligaments in ankle crashing out Morgins way or some outer bumble PdS region, long one legged cycle back...remember you pay for EVERYTHING with French Dr/pharmacies, you have to buy your own crutches, medication, bandages and dressings. Oh and most local Dr's can X-ray you but you still have to pay a couple of hundred quid up front for that!!!
So get insurance .. although unfortunately I cant' recommend a company as I get it through work!! Just trying to point out importance of it as this is another long running debate. oh and mate helicoptered out of Les Gets bike park in about 2005 or the likes .. it would've cost him thousands ..except any accidents within the park were sponsoered and paid for by Kona..result as he had no health insurance just the E111 he would've been screwed!