I don't see much benefit from the French model. Many of these systems are just consequences of how each nation moved to a universal healthcare model. It's good if you were American looking for an alternative system but I am not convinced what it would change for us would be worth overhauling our system.
The main differences are that most of the cost is underwritten by the state at the point of use but there are charges for minor medical treatments which can be claimed back from the state and/or supplementary healthcare insurance that you get automatically from work or you pay for.
The most positive difference is that things like dental care are included in that supplementary (it's NOT private) insurance. So that works out cheaper. The main drawback is some things are not free at the point of use which I do not think you could sell to the public. The reimbursement system is automatic if you have your healthcare card.
But all of these amount to you paying more for healthcare. France spends more per person on healthcare, people on average pay overall for healthcare. They spend a lot more.
https://www.health.org.uk/news-and-c...he-past-decade
Either way, you'll be paying this with taxes, with 'additional' insurance or reduced payroll because your employer pays it.