All of the above, plus some more.
The Communist Party was very powerful in its own right, class war was still raging at that time, with the hugely numerous workers feeling that they were not well represented by the 'fat cats' in the governments and wanting rights and some protection from the free capitalism those in power encouraged. Those workers believed that the Communist Party was the only one which could represent them and fight for them against the power of the 'fat cats'. Before the war the Communist Party was an illegal organisation in many European countries but after the war they couldn't be pushed aside and ran for the elections. The number of factory workers, miners and low class workers did the rest.
As well, after Hitler invaded Russia the Communists in the occupied country turned against their ex-allies. As they already had an underground structure in place - set up when they were an illegal organisation - they quickly became a very effective fighting force and by the end of the war a very powerful one. Many people saw them as heroes and thought they could impose a quick fix it to all the problems plaguing war torn countries. The actual governments feared them because they were so powerful. The orders the Party received from Stalin was quite simple: take power, anyway you can, civil war included. That threat was enough to make those governments back down from a confrontation they knew they had good chances of losing.
That was why De Gaulle immediately came to Paris once it was freed and did that walk down the Champs Elysees by the way, he knew that the Communists were readying their take over and were in fact getting ready to greet him as the de facto rulers welcoming a war hero. He cut them at the knee in such a way that the civil war that was being readied never happened and he gave the death blow to that attempt by forcing the FFI to be swallowed up by the French army instead of staying an independent power.