Germany has private and federal insurance. You have to be insured in either one of them. Still, private insurance is not insanely expensive, the main downside is that you generally have to foot the bill first and then make a claim to your insurance carrier. The upside is that doctors know they get their money for everything, even the "unnecessary" tests, so you get preferential treatment like less wait times for medical imaging and such which is a constant point of contention and discussion as it somewhat introduces a medical caste system.

What makes the German system way less toxic tho is that insurance carriers cannot just deny your claim with bullshit cop-outs like "out-of-network hospitals" or such. That doesn't exist.

France has some. They offer refunds on things that the public one doesn't support, and you will need some of them a few times in your life. I would guess something around 800€ was spent on me for non-refunded stuff thus far. It probably wouldn't justify getting an insurance, but it justifies their existence