Actually I found France has a very high ratio of doctors to patients. A shorter waiting time seems very likely. The doctors pay very little for malpractice coverage and make about $55,000 a year. The tax rate is 40%, but much of that is not paid by doctors as part of the plan. Also, most of a doctor's education is government paid. Unlikely such a plan would work here.
Indeed, the existence or non existence of a national health insurance program is irrelevant to the cost of health care/insurance. In wealthy countries that have substantially lower health care costs than the US, the governments achieve lower health care costs by mandates lower reimbursements to health care providers.
The less health care providers are paid, the lower health care/insurance costs are with or without a public plan of any sort. There are two ways to lower payments to health care providers. We can do it the way Canada and some other countries have by not allowing providers to charge more for covered services even if consumers are willing to pay it, or we can get rid of archaic federal and state laws that limit price competition in the health care markets, specifically by passing a law to allow insurance companies to sell national health care policies and by amending ERISA so that workers can use the company's contribution to by individual policies instead of being forced, as the present system requires, to buy a health care policy that was designed to serve the company's interests rather than the worker's interests.
These two steps would greatly increase competition in all health insurance markets with insurance companies putting downward pressure on providers in order to maintain profits as consumers sought the least expensive policies that served their needs, but companies that paid too little would find few providers wanted to do business with them, so that by increasing competition in this way, free markets would find the lowest sustainable health care costs that would not require us to sacrifice quality.
On the other hand, in countries like Canada that used coercive legislation to lower health care costs the lower costs of health care are subsidized by consumers who must endure months of pain and suffering while waiting for back surgery or joint replacements and other care the government deems non urgent, and cancer patients must endure the older anti cancer drugs that will do the job but cause much more pain and suffering and collateral damage than newer ones. And even France, which has much higher health care costs than Canada has, although lower than the US, is finding its low rates of payments to health care providers is causing a too low rate of capital investment so that it may soon have to start raising taxes or turn to longer wait times and less advanced medical technologies as Canada has been forced to do. France is now trying to stretch the euro to put off the time when it will have to do these things by encouraging primary care physicians to limit access to tests and specialists just as Obama has proposed doing in his "rewarding quality not quantity" sloganeering.
Obviously, it makes more sense to leave health care and health insurance costs to negotiations between consumers and providers in free market negotiations than to leave these decisions up employers or to politicians who are seeking to please one or another special interest group.