If you don't have this insurance (mutuelle), the State does provide the social security (it's provided either way, the mutuelle is on top of this).
But this is basic social security. If you're in a car crash or something, you're mostly covered. If you need work done on your teeth, you're on your own.
When I needed to spend the night in a hospital after breaking my wrist, basic social security covered the ambulance and the actual procedure of putting my arm back together, but had I not had a mutuelle, I would've been on the hook for the hospital stay.
It may be a bit more (would need to dig the bill but it was of that order of magnitude) and I am writing this do that a non-EU person does not get the idea that it was 1000€ a day or something.
Only 50%, no?
Also, in Germany the cost of insurance is tied to income. So I went from the bizarre situation where I went from paying ~500€ while employed to less than 200€ now that my business is not generating substantial revenue.
We are (again essentially) talking about taxes, just calling it social insurance.