As much as I usually love to hate on the French system, it's hard to describe to someone who never experienced it the feeling of security that comes with the knowledge that every treatment decision for you is made by your doctor on the basis of best medical outcome, period.
Never before I moved to the UK and discovered private insurance through work had I even heard about "preexisting conditions", "lifetime limits", and the whole idea of having to talk to some guy in a call center about your ailments to get pre-approval, which you might or might not get based on whether this will affect their finance guy's Q4 targets.
Oh and "inefficient health care system"... absolutely, if by that you meant the US system : https://www.bloomberg.com/news/articles/2016-09-29/u-s-healt...
Americas healthcare is not truly private either - there's a lot of state intervention in it. They manage to get the worst of both worlds due to the inefficiency of the federal government.
This ignores the much lower price of consumables in the US as well.