The American mourning of the 9/11 :
In 2003 / 2004, French troops had twice the opportunity to kill bin Laden, has they got him into the crosshairs.
However, they have not had the "green light" from the U.S. command, as Bin Laden had to be arrested or killed by U.S. troops.
Bin Laden dead or alive :
With the near-to-come U.S. presidential elections (end of 2012, but the primaries are about 1-year long, bringing to end 2011) and B. Obama in trouble in the polls following his "social" policy, it was politically important to end this hunting.
Bin Laden, a source of risk :
Capture bin Laden alive would have required years before he was found guilty. The capture by the "West" would have been subjected to a high risk and bloody pressure of terrorism, while by killing him, the U.S.simply encourage Al Qaeda to "end the story" ...