But two citations don't begin to tell the whole story. Some deeper Googling returned zero hits on "French health care crisis", which, given that the article you found came from 2004, suggests that the crisis never materialized. There was a similar paucity of bad news from the UK; again, the article you found seems to be an anomaly.

A broader search on terms related to "health care crisis" and France didn't return anything substantively negative about France's health care system, aside from purely ideological denunciations. What I did find was in fact overwhelmingly positive, not only about France but about European health care in general. This graphic is a nice summary of the piles of statistics:

The Health Care Crisis and What to Do About It, Paul Krugman, New York Review of Books, March 2006

One way to interpret the table is to wonder how it could be that if France is having trouble financing health care, why hasn't the United States already gone bankrupt spending twice as much per capita? Seems to me that if we adopted France's platinum health care system we'd spend half as much and get incrementally better results from it.

Dude, we'd save money going to "socialized medicine"!

I found a quote that, while it doesn't try to bandy about statistics, provides the most commonsense take on the issue I've ever read:

If our health care system was the envy of the world, other nations would duplicate it. That, instead, all those who can afford first world systems have copied the European model really says all you need to know.

Ezra Klein