This is a great question. De Gaulle separated himself from NATO for a variety of reasons. The US government did not share their nuclear know-how from the Manhattan Project with the French. Moreover the "special relationship" between the US and Great Britain that gave the UK the Polaris SLBM particularly galled at him (terrible cheap drive-by pun but applicable). Add even to that: his country was forced to develop its own nuclear deterrent. In 1966 the United States had the Polaris A-1 SLBM. This was a comparatively short ranged SLBM. The Minuteman ICBM was just establishing its credible notoriety, having been first deployed in 1962. By playing around with /u/restricteddata's map "MISSILEMAP" one can see that American SLBMs were within credible range of Soviet strategic assets like submarine bases and coastal cites, but not much more. (A sub would have to be posted in the Baltic Sea or in the Arctic near Murmansk to hit Moscow with the A-1) This was better than nothing. Later on the Polaris was better able to hit inland targets. The British had access through the Polaris missile agreement for the first generation of Polaris well as later ones while France was left high and dry. Being left "out of the loop" played a huge role in French animosity to NATO.