That, my friends, is a myth. The real story.
In reality, per-capita state-sponsored health expenditures in the United States are the third-highest in the world, only below Norway and Luxembourg. And this is before our new health law kicks in. (The U.S. appears second in the chart because we only have 2008 data for the Luxembourgers):
In 2009, according to these statistics, which come mostly from the OECD, U.S. government entities spent $3,795 per person on health care, compared to $3,100 per person in France. Note that these stats are for government expenditures; they exclude private-sector health spending.
If anything, the U.S. figures understate government health spending, because they exclude the $300 billion a year we "spend" through the tax code by making the purchase of employer-sponsored health insurance tax-exempt.
So: if we measure the relative freedom of health-care systems by the dollar amount of government involvement in health spending, the French system is actually meaningfully freer than America's.