They're not free, you're paying 60% minimum of your income in taxes and a good part of goes to social security. Not only is that not free but it's extremely expensive. And hospitals are not the best either, in fact I'd avoid them if I were you if you care about not getting nosocomial infections, they're famous for that.
My son was born very prematured (6 month), he was born at Port-Royal in Paris (APHP, French public hospital), the total cost of his birth was 320k€, I did not even issue my credit card ONCE. Paid by public money. Period.