Intelligence is not an exact science. Because you are often dealing with information that the other side is taking active steps to protect, belief (based on the best available information) is what a policy maker has to deal with.
It continually amazes me how it was irrational to operate on the assumption that the CIA was correct with regard to WMD in Iraq when it was an issue they had been dealing with for over a decade and was the belief of every major intel agency in the world but at the same time irrational to operate on the assumption that they were wrong with regard to Iraq and AQ since the relationship between Iraq and AQ is still debatable.
Iraq did have contact with AQ prior to 9/11. AQ operatives were openly operating in Baghdad prior to the war. Was there an operational relationship? We still do not know.
The French did not have intel that differed from the US/UK, nor for that matter did Russia, Germany, Israel, or China. The difference was not in the intel but the belief in what an appropriate response to that intel was.