Our system is not that simple either.
- you have mandatory health insurance which is a percentage of your income
- you have an extra insurance (called mutuelle) which you may not have if you are not salaried (but that you get anyway), or it may be compulsory if you are salaried.
Doctors can be in one of the two groups: 1 or 2. 1 means that your costs are fixed and regulated by law. This is for instance 25€ for a general/family doctor visit. n% of this is reimbursed by the compulsory insurance, and the other one reimburses the rest. n depends on the medical act - for instance for the visit to the MD n=70.
The group 2 fixes their prices as they wish. This is usually for specialists (but not always, there are plenty of specialists that are in the group 1)
The extra insurance covers up to M times the regular cost. M depends on the act and on the insurance.
Generally speaking - the more serious the act, the more you are reimbursed. A heart operation will be free no matter what, but something simple may cost a lot (more that the extra coverage). It is very rare, though, to go over that extra coverage.
Dental is not covered very well - it is OK for small things but implants fo instance are notoriously expensibve (you may pay, say, 1000€ out of 6000€). So is optical (you can always get glasses for free but they will not be the best ones).