There are a number of other western countries that have private healthcare systems. The difference between their and ours is tight regulation and cost controls, often combined with a robust public option for the unemployed to fall back on.

I should add that in France, you can keep your employer health insurance for free for one full year, in many cases when you lose your job which limit the risk of a "hole" in the health coverage.

France has private supplementary insurance programs in addition to the state run health insurance program.

A good corollary in the US is Medicare: everybody over 65 can enroll in Medicare Part A for free, but you can also choose Part B, Part D, and "medigap" coverage, each of which is optional and has a monthly premium.

There is a "baseline" provided by the state, and the employer health insurance adds extra coverage.

It's still tied to working and your employer pays to the pool.