There are two systems for reimbursement - public and private.
On the public side, the government decides how much any treatment / test / medication etc 'should' cost, and will usually reimburse up to 70% of the cost to that level. People on low income get 100%. It's means-tested, which is the norm here and I really can't understand why the UK is so resistant to it. Also, Drs / specialists can decide which 'tier' they want to offer - and you can choose a lower tier Dr to keep closer to what the govt will reimburse.
On the private side, virtually everyone has a 'mutuelle', which is insurance that pays the difference between what the govt will reimburse and what it actually costs. Mutuelles can be anything from basic to bells-and-whistles, and which one. you choose depends on what you want / can afford to pay, and what your employer will contribute.
If you are in work, your employer is required to pay 50% of the cost of a mutuelle. So DH's employer pays 52,99€ of his mutuelle, meaning that he pays €52,99 per month directly from his salary. For me and our two boys we have a separate policy and we pay €115 per month for us three. These are top-end mutuelles, meaning that the reimbursements are very generous. We have had multiple surgeries over the years (all done in private clinics i.e. single en suite rooms), hearing aids, glasses, orthodontic and dental treatments, multiple physio sessions, childbirth and wellness checks throughout their childhood, annual gynae rdv - you name it. All done in a timely manner, all in clinics / practices within a short distance of our home, all at a time of our choosing - and virtually all reimbursed. I think the most expensive thing we've had to fork out for has been dental - DH had to have multiple (I think 6 or 7) old fillings removed and modern crowns put on - that cost a few hundred out of pocket. I think when I gave birth to DS2 I as in a private clinic, own en suite room, for 5 days (it was a complicated birth), and I think I paid €40 out of my own pocket - the govt and the mutuelle covered everything else.
Again, there are no-cost and very low cost mutuelles, often offered by charities and other associations set up specifically for this purpose, for people on low incomes. French grannies do not end up dying in the street, unless they are really unlucky.
The healthcare system here is just miles ahead in so many ways. E.g. because most services are essentially private, they can be set up wherever the practitioner wants to - they aren't tied to some monolithic out-of-town hospital with terrible parking. I'm city centre, tbf, but within 10 minutes walking distance of my front door I can access my physio (and many others), my GP, the private clinic where we tend to elect for surgery, my gynaecologist, walk-in laboratories for blood and other tests, multiple midwives / nurses / physios / psychologists, imageries (clinics that offer MRI, X-ray, scanner, echography). I can book rdv at any on these online, at my convenience. And yes I might pay up front but it is reimbursed generously and way in excess of the mutuelle premiums that we pay.