Supposedly the 'anarchist' movement would have been successful in France and thereby the Communists would have been able to take over France after the anarchist weakened the state, right?
According to the communists, this is a wrong supposition. They didn't think that the movement could actually bring down the French state in May 68, and I think they were more or less correct.
That, plus what Red Star said - the Commie bloc was afraid that this could easily spill over into their own countries, and they didn't think that the majority of the movement was under sufficient communist leadership.
Finally, and perhaps the most importantly, since the dissolution of the Comintern in 1943 (and probably starting even earlier that that), the Communist movement was becoming increasingly conservative, and as you may recall, Khrushchev officially declared a doctrine of peaceful coexistence between east and west, the era of Detente. Due to this, the PCF, along with the rest of European communist parties were becoming increasingly less revolutionary and much more integrated and subordinated to their States. Hence they did not support an anti-state movement.