There is obviously no anarchy in France. What you mean is the civilian unrest, caused by the despair of young immigrants (mostly in the third generation) in the banlieues (the suburbs), who don´t have chances to get a job or being part of French society. After years of being ignored, now they are happy to get the attention of media stations around the world. Although this seems to be a national problem of the French, it definitely isn´t. Townships in South Africa, Favelas in South America, Ghettos in Europe and North America. Of course this was a special situation, because the people of the banlieues in France never had the feeling that they were Frenchs, even when they became French by law. The despair bursts after the remarkable statement of the French secretary of the interior, Nicolas Sarkozy, who characterized those people as ragtag. I recently spoke with some young Frenchs and they were very angry about this statement. Unlike some German politicians I don't believe this couldn´t happen here too. I believe this is a general problem of modern economy.
I think the French can handle this problem.
Ironically some French TV-Stations called the unrests in New Orleans as may be the beginning of a civil war, which now echoes in some American commentaries.
But now back to topic:
"Anarchism is a generic term describing various political philosophies and social movements that advocate the elimination of all forms of government, in favor of a society whose members interact on a voluntary basis. These philosophies use anarchy to mean a society based on voluntary interaction of free individuals, and the idea that communities and individuals have a say in decisions to the degree that they are affected by their outcomes." (wikipedia.org)
I don't believe that Anarchy could be working. With Hobbes words it would end in a "war of all against all."