@Olivier5,
They did indeed. Frankly we had better working relations with the French military than the British, though the French usually wanted to keep the cooperation invisible. I often found French attitudes and outlook to be much more similar to our own that those of the British - we both think that we are the center of the world and that everyone should speak as we do.
About five years earlier, soon after the simultaneous 1983 Beirut bombings of the barracks of French and U.S. forces in Lebanon, I was an Air Wing commander on a carrier in the Mediterranean, and we, without any fanfare or notice, started joint operations with the Air wing on Clemenceau, Joining up their Etendards & Mirages with our A-6,A-7 and F-14 aircraft for coordinated rendezvous, tanking communications exercises - all then very unusual. I was the flight leader and, later learned these were rehearsals for a joint retaliatory strike. After two such drills we were ready to go, awaiting only specific targets.
At the last minute, as we joined up at sea for a prestrike joint briefing onboard our ship , our political leaders pulled out of the plan saying (to us) that they had no targets that reliably included the perpetrators. I still recall my French counterpart's reaction "c'est une question d'honneur" he said with dismay.
The French a week later went ahead with their own attack. We should have been with them.