I don't think that disproves a general trend that increased socialization in healthcare costs leads to better outcomes and less per-capita spending.

Also FWIW France and Switzerland both have universal healthcare, under different systems where France splits payments 3 ways and covers more with the govt[1], and Switzerland seems to have a system like the ACA in the US where it's compulsory, but they also set caps on the deductibles and maximum price.

[1]: https://en.wikipedia.org/wiki/Health_care_in_France

[2]: https://en.wikipedia.org/wiki/Healthcare_in_Switzerland

Private healthcare in France is supplementary to public healthcare and mostly abides by regulations dictating what can be reimbursed by the social security system, there's quite a bit of price control. It only gets wild in niche products (say very fancy dental implants).

Those countries both have "less generally" than the USA.