People say 'Europe', speak as if their experience is the same across the continent, and anyone with a different experience is somehow not in the Europe they mean. It's very annoying.
European healthcare is run very differently across the continent. 'Insurance' can mean a [state] social insurance institute that the doctor must bill. Some countries would employ the doctor directly as part of a nationalised health system. Some places it might be the municipality or city that would then get some subsidy from central government. Some it is a mix of all of this. 'Free' healthcare might actually mean a few hundred Euros, or literally nothing.