I was reading about NATO in the cold war, specifically about Frances role. Although they forced NATO troops out of France in the 1960's, Wikipedia claims that there was a plan to fully reintergrate the NATO and French forces called the Lemnitzer-Ailleret Agreements. What were these?
The Lemnitzer-Ailleret Agreement was made between French Army General Ailleret and The Supreme Allied Commander Europe(SACEUR) General Lemnitzer. The French General wanted complete withdrawal of French troops from the NATO forces. The SACEUR General wanted to reduce the impact of French withdrawal especially in the French Zone of Germany. The agreement ended up with French forces remaining in the FZG but the role of the French changed. Now the French Were no longer part of the NATO defense force but took a counteroffensive role which was seen as more valuable to NATO. This role allowed France to seem to keep its independece from NATO while still being part of the NATO forces, and this agreement was kept top secret for around 20 years for that same reason. So it wasn't exactly a full reintegration into NATO but it did keep the French involved in the NATO armed forces.
Source: http://www.defenceviewpoints.co.uk/articles-and-analysis/france-s-changing-role-in-nato