The French also believe that their century of experience dealing with Arabs in North Africa, even though they abandoned their last colony there, Algeria, in the 1960s, gives them better insights and skills. At least when it comes to dealing with Islamic radicalism.
Finally, France has had to deal with some very active Algerian terrorist groups over the last decade. These groups were more effective in France because of the millions of Arabs living in the country. Many of these Arabs support Islamic radicalism, and have provided cover, and other assistance, to Islamic terrorists.
The French believe that invading Iraq was a mistake, because it just stirred things up, with the Arabs (in France, and throughout the Middle East.) Part of this is the usual French arrogance, blindly believing that whatever methods they have developed must be the most efficient, and that any other approach is obviously second best and defective. Islamic terrorists have not pulled off an attack in France since 1996. However, despite their smugness, the French are alarmed at the growing threat from among their own Arab and Moslem immigrant population. But this is a problem that has been growing for decades, and France has not been able to come up with a solution. Unlike the United States, France does not encourage assimilation as much. Thus, while France has better tools to deal with terrorists, the United States has a better social system to prevent them in the first place. Thus the United States can go into Iraq and cause far less danger back home. This, of course, makes the French furious. Invading Iraq may help the United States in the long run, but it just causes more problems for France, and other European nations, in the short term.
France believes it is better organized and equipped, than Britain and most other European nations, to deal with Islamic terrorism. There are three main reasons for this attitude. First, France has a government system that concentrates much power at the center (like most European states), and there are few legal constraints concerning individual rights (in sharp contrast to the United States, Britain and Germany.) French law is fundamentally different. If accused, you are guilty until proven innocent. French prosecutors operate much like police commanders, deploying investigators and police during the investigation and prosecution of cases. This different attitude also enables French intelligence agencies to operate with more speed and efficiency.