Stalin lives to 1956, shortly before the Suez Crisis. A nasty power struggle ends with Beria on top, just as the British, French and Israeli's a contemplate military invasion of Egypt. In order to force back the Red Army, who moves to overthrow the shaky NVKD head, Beria forces Soviet military into Egypt in order to prevent a Western invasion. The U.S. remains by its anti-colonial stance OTL but just as the British and French prepare to attack Egypt, the house of cards falls apart in the Soviet Union with an attempted coup blossoming into a low-key civil war. The overjoyed colonial powers invade Egypt quickly with such news, effectively distancing themselves from the U.S.
Fast-forward to the late 60s. NATO is no more (effectively reduced to Germany and a few ex-Warsaw Pact countries) and France is under a loose military junta as it struggles to hold onto Algeria (a claim recognized by few outside of Europe). The U.S. funnels arms into North and West Africa through Yugoslavia in an effort to undermine colonial interests there. While Britain hasn't entirely broken with the U.S., there is major contention about the future of the Special Relationship. France is a different story, more than willing to reassert itself as a great power. When the French detain a ship inbound to Yugoslavia holding American arms, General Salan sends an ultimatum: cease all arms funneling and pay indemnities for French losses in the Algerian crisis. President Nixon's refusal to cease its activity in the Mediterranean and respond to the call for indemnities results France declaring war after opening fire on a trade ship.