From Strategy Page comes this short article discussing pre-Iraq war diplomacy. The short version: France would have contributed to the Iraq invasion if the US had given it a sphere of control. Here's the excerpt:
France was not always opposed to the American invasion of Iraq. One persistent Pentagon rumor, however, might explain why the French came to oppose the overthrow of Saddam Hussein's dictatorship. In December 2002, a French staff officer visited the Pentagon with a proposal from his government. France would send 18,000 troops (about what they contributed in 1991) to join the Iraq invasion force. However, France wanted a specific area of occupation after the war, with full authority in that area for as long as Iraq needed to be occupied. The American State Department backed the French proposal, but the Department of Defense didn’t trust the French, and were suspicious of their motives. So the French officer went home empty handed, and the French government decided that invading Iraq was really an evil thing to do.
If this is true, it is further proof of French perfidy and duplicity. Remember: the French backed Saddam and the Sunnis for more than 30 years. That allegiance meant more to the French (and still does) than any alliance with the US.