The French system has been having money problems longer than the recession. Here is an article about the French system.
It is mostly positive, but they do pay 40% if their income for it at this time, and that is not enough to cover the costs.
This article says they have run a deficit since 1985:
I just wish journalists would do their research. I don't know where they get that 40% of the income goes to healthcare. The contribution is 19.7 % of taxable wages, the employer pays 12.8 %, the employee pays 6.9%. In Germany the contribution is 18.5%, half is covered by employer and half by employee.
It is not a perfect system and the reason why it runs deficits is that both in Germany and France people who have no income or don't work receive full health care benefits without having to pay anything.
Despite of that Germany spends 10.8 % of the GDP on health care, has everyone covered, with much better outcomes. The US spent 16 % of the GDP on health care with half of its citizens covered, not to mention the underinsured and bankruptcy of people when they get sick and peope dying because they can't get treatment due to lack of insurance.
I think the US is the only country where I go to the doctor and pay my co-pay and then I still have to pay deductibles which I don't know how much at the time of buying. That's one heck of a business model.