Well, the eventual overthrow would still happen. The youth and workers were just to dissatisfied with the Gaullist government. The May 3. strike was just the trigger for the innevitable revolution.
If you want the old government to stay in power, you have to go way back to the late 50s or early 60s. With a stronger centre left 'Socialist Party' that goes for good old Bismarckian crack down pollicies, you could avoid the rise of the new left and in consequence the revolution. Therefore the CIA backed, Neo-Fascist dictatorship that overthrew the PCF government a year later and stayed in power up untill 1978, would be prevented. France would stay more Gaullist and a burgeoisie democracy during the cold war. Its alliance with the US may be more passive. Todays france would be less left leaning, as the modern left trend resulted directly from the 'Summer of Marseille' (when in june of 1978, a general strike that started in Marseille spread to all of france and the military refused to shoot on the worker, which forced the fascist government to abdicate).
Italy is a different story. The Italian revolution was of course inspired by the french one, but they also acted very independent. Its quite possible that the 'Italian October' would still happen in october 1968, and would still be crushed by the CIA and Italian military.
But it could also be butterflyed away, with a weaker new left and the lack of the 'French example'. The links between the Paris May and the Italian October are still debated by historians today, so we dont know for sure.
I think the Cold war would go down mostly like OTL but with the US having an edge in prestige without their analogues to Hungary and Czechoslowakia.