The meeting in the bar was contrivance for sake of plot and drama and all the other good things that make a movie...a movie. Mercenaries were common in the conflict, and served as the backbone of the Katangan rebellion, and many of them did come from France, but also Britain, Belgium, and Germany. The mercenaries were the most effective fighting force that Tshombe had, being veterans of the Second World War, Korea, the French war in Indochina, Algeria, and other, earlier, colonial conflicts.

French mercenaries were in Africa and did serve in the Congo, and in significant numbers.

In this answer, I speak specifically to the accuracy of the character of Rene Faulques.

I also go on, here in detail, on the actual efficacy of mercenaries, their role, their numbers, in the Congo as well as later, in Angola.. In this post I do give something of a breakdown at certain points as to the national composition of the mercenary forces.