But France is not a country where medicine is the most "socialized". For instance, GPs are usually private doctors in France. Then the universal health insurance refunds 70% of the price usually (but it can be less, because doctors can choose their price - it's called "sector", and only ). Then, most French people have a complementary private insurance called "mutuelle" from their job that pays the remaining 30%. Only long-term illnesses such as cancer are fully reimbursed by the national health insurance.

And yes, even the least paid doctors in France earn much more than the median French salary. Also in France, medical school is not expensive ("socialized" education). It just takes time...

https://en.wikipedia.org/wiki/Health_care_in_France