In 1966, French President Charles De Gaulle, displeased with the US response to a request for a tripartite directorate putting France one equal terms, withdrew French forces from NATO. Seeing as WWIII never happened, and the French had made secret agreements with the US for rapid reintegration of military forces in the event of war, did French withdrawal really have a significant effect on NATO capabilities?
Withdrawal from NATO has always been a very symbolic gesture. It basically meant "France is the ally and friend of the USA but we refuse to be treated as a subject". De Gaulle wanted the NATO to be an alliance of like minded nations that get each other's back and are on an equal footing in the decision making, the US saw NATO as a western equivalent of Warsaw pact, with the US as the center of it protecting the other members from the big red ogre.
There was no doubt though that even though De Gaulle did withdraw from NATO France would join its US ally without question in the case of a war. The USSR was absolutly not fooled one second by this withdrawal.
One could even argue that this withdrawal actually good effects on the NATO military strength as the French began immediatly to develop their very own nuclear arsenal as a result to take their protection in their own hands instead of relying only on the US defense budget for that like most NATO nations did.
A presidential directive from De Gaulle himself explained in 1961 (five years before the NATO withdrawal) that "within ten years, we will have enough firepower to kill 80 millions Russians, well I don't think one would easily attack a people with the capability of killing 80 millions Russians, even if they have the capability to kill 800 millions French people, providing these 800 millions French people existed".
The same directive from the 16 December 1961, the objective of France was to have the capability to wipe out 50% of Russian economical assets.
It means that additionally to the US arsenal that was intimidating enough, the USSR faced a second smaller one that could inflict huge damages on them as well.
France never withdrew from Nato, it withdrew from the integrated military command, which means US control.
Instead of being in an integrated military command (ie a Nato chief - usually US officer - ordering French troops what to do) the troops were just simply part of the political alliance (ie Nato chief would request something to French troops, ie the final decision power being left in the hands of the French military).