The Communist Party was very influential but the government after the war was center-left and Republican (in the French sense of the word), and the political program agreed upon by all the political currents that formed the Resistance was a compromise across the entire spectrum (the Resistance started on the very right and integrated Communist elements after the USSR went to war with Germany). While it pains people to acknowledge it, the Vichy government itself passed a lot of social reforms prior to 1945.
They were a social and ideological force to be reckoned with but they never really went into power, De Gaulle saw to that.
The party line of the French Communist Party in the 1940s was Stalinist. It wasn't until the Soviet crushing of the Hungarian uprising in the following decade that French Communism saw a schism between pro-Soviet and anti-Soviet sides.
The USSR may have saved Europe from Germany, but the USA saved Western Europe from the USSR. The French in 1945 were likely aware of this.