France never left NATO. It remained a full member of the North Atlantic Council but did, in 1966, leave the NATO Integrated Military Structure. It thus ceased to have a MilRep on the Military Committee at NATO HQ, but did maintain active observer status. Sensibly, taking account of its geography in relation to the potential Soviet threat, a number of General to General agreements were then drawn up to ensure that, should war break out, Allied defence could still be conducted. Given changing circumstances, France rejoined the Military Structure in 2009. This link may prove useful:
France and NATO - France-Diplomatie - Ministry of Foreign Affairs and International Development