Communism had broad popular support in most of Europe immediately after the war, maybe not a majority in most places but a substantial number of people in post-war elections and power struggles supported the communists.

The main reason for this is the political establishment of these countries was pretty thoroughly destroyed among the former axis powers and the countries which had been pro-axis or axis occupied during the war. The political forces which emerged were generally those who had resisted fascism during the war.

In France for example the communist party was part of the three party alliance between themselves, the moderate socialists, and the christian democrats in the period right after the war.

There was some effort at maintaining similar popular front governments in the east and west, but relations between the 2 sides got worse and each side began exerting heavy influence on the territories it occupied.

In each nation there were communists and anti-communists. Its hard to say what would have happened if somehow each country had been able to hold a free election without influence from the west or east.

There were only a couple basically free elections in the eastern european nations. In Czechoslovakia the communists won a pretty convincing mandate in 1946 but a coup removed the opposition altogether shortly thereafter. In Hungary the communists lost the elections quite badly in 1945 and the next round a few years later was rigged for the communists.

It is also difficult to know exactly how much of the responsibility for the various communist coups belongs to the occupying russians and how much belongs to the local communists. This varies between countries but the communists were probably most popular in Yugoslavia(which basically liberated itself), Albania, Bulgaria, and Italy. They were much less popular in Poland, Romania, and Hungary.

In the end: the fate of each country after the war was mostly determined by the occupying Americans, British, and Russians. The location of the iron curtain paid little mind to the sentiments of the people in each country.

I cannot say much about the countries you mention, other than to note that in every case communists did have genuine and in some cases popular support as well, but perhaps the Finnish experience could be enlightening as well.

Finland had agreed to an armistice with the Soviet Union on 4th September 1944, avoiding Soviet occupation but agreeing to expel the remaining German troops from Lapland. While this "Lapland War" was still going on (it would be concluded on 27th April 1945, as Finnish troops reached the Norwegian border), the first post-war general elections were held on 17-18 March 1945. These were the first elections in Finland's history where the Communist Party could be voted for openly: soon after Finland's declaration of independence in late 1917, the country had fought a particularly vicious civil war between the Reds and the ultimately victorious Whites, who had promptly banned all parties left to the moderate wing of Social Democrats and executed, jailed, or driven into exile many of their activists.

The lifting of this ban immediately resulted to the 1944 founding of the Finnish People's Democratic Union, or SKDL, a left-wing umbrella party that was in practice controlled by the now legal Communist Party, although many of its members and representatives were not communists.

At the same time, the Allied Control Commission that was placed to oversee that the terms of the armistice were complied with had banned from politics the fascist Patriotic People's Movement party (IKL in Finnish) and its eight members of the parliament, as well as eleven prominent politicians who were deemed to be too friendly to Germany or too supportive of the war.

The end result of the elections, where by now discharged veterans voted very actively (the ongoing Lapland War was fought mostly by younger conscripts, who hadn't participated in the wars against the Soviet Union, and were mostly below the voting age of 21), was a stunning victory for the Left. The radical leftist SKDL came to within one representative of being the largest party in the 200-member parliament; however, the largest party was the Social Democrats, who despite the loss of 35 seats did retain 50 seats. With the addition of one MP elected by the Swedish-speaking left, explicitly left-wing parties were therefore only one vote shy of majority at all times. With the centrist Agrarian Union holding another 49 seats (down from 56 in the last pre-war elections) and right-wing and conservative parties being in minority, the body politic had shifted decisively to the left; as one leftist author noted in 1945, this was the end of the "first republic" and the beginning of the second.

In other words, as in Great Britain, France and Italy at the time, Finnish veterans and the general public had been promised during the war that their sacrifice would be remembered, and now they wanted to make sure that this would indeed happen. While the elections were held in an atmosphere that certainly was to some degree ominous - there were real fears that the Soviets might nevertheless occupy and annex Finland - the elections themselves were by and large free and fair. Therefore, it is clear that the radical Left had considerable popular support, and left-wing policies in general held majority support. This was reinforced in 1946, as two Social Democrat MPs defected to SKDL.

However, Finland did not turn communist. The radical left had wanted to follow the strategy used by Eastern European communists and "fold" the other parties into a "popular front" led by communists post-election, but the Soviets forbade them from doing this in Finland. In 1946, the Central Committee in Moscow ordered Finnish communists to prepare a revolution, but the party could not execute. Their network of activists, which had never been that strong, had been further disrupted during the war, and their voters were for the most part not keen to support a revolution. Even though a communist, Yrjö Leino, was placed as a Minister of the Interior, thus controlling the police (an appointment that was menacing to say the least), and letting the communists create a short-lived "red" secret police, he was an alcoholic who either could not or did not want to help with a coup. Furthermore, radical socialists had promised much, but once they were in the government, they could not fulfill all of their promises, resulting to some disillusionment among the populace. SKDL also opposed easing the terms of the onerous peace treaty, which definitely did not endear them to Finns, and led many to conclude that the party was little more than a Soviet puppet.

Later assessment is that the communists in leading positions of the SKDL were fully aware that they could not stage a coup d'etat without direct intervention by Soviet military forces. Nevertheless, there was widespread fear that the Finnish communists were plotting a revolution, and these fears were intensified after the Communist Party of Czechoslovakia had seized power (with Soviet support, despite receiving record-breaking 38 % of the popular vote) in February 1948.

Finnish communists hoped that the Friendship, Cooperation and Mutual Assistance Treaty (FCMA), which was being negotiated in Moscow, would give them the means to call in Soviet support for a revolution. The treaty was to be ratified by May, and in April 24 1948, the SKDL's party newspaper printed a speech from a noted communist Hertta Kuusinen; the headline was "The Czechoslovakia's road is our road". The following day, the party newspaper of the Social Democrats, who had became the most implacable enemy of communists due to their capability to address the same working class population, publicised what the paper claimed was a Communist plan for coup d'etat with Soviet support. The consensus today seems to be that this was more an exercise in wishful thinking by some communists than a serious plan, but the possibility of a take-over was taken so seriously that the army deployed artillery and armor units close to Helsinki on the night of 26-27th April. The ratification hearings of the FCMA in the FCMA treaty began on 28th, and the president finally ratified it on the 30th. No coups materialized, however.

A representative of the Finnish communists subsequently traveled to Moscow and presented allegations of a right-wing conspiracy to prevent the FCMA treaty from coming into force, and begged the Soviets for help. The response was icy: Andrei Zhdanov, the rumored successor of Stalin, told the representative that the Finnish communists were useless, as they continuously relied on Soviet aid rather than standing on their own. No support whatsoever was forthcoming, although IF the communists could take over, then the Soviets could help them retain power.

This was the high tide for revolutionary communists. The communist minister of the interior Leino was ousted in summer, after his actions in the deportation of 19 Russian emigrants to Soviet Union in 1945 led to a vote of no confidence. SKDL suffered a defeat in the parliamentary elections of July 1948, losing 11 seats while Social Democrats, the Agrarian Union and conservative Coalition party gained seats. Never again were the communists in such a propitious position for a take-over. The years between 1944 and 1948 have been subsequently called the "years of danger", even though fears of imminent coups proved unfounded.

Key source used is
Nevakivi, J (2006): Jatkosodasta nykypäivään. In: Suomen poliittinen historia 1809–2006. WSOY.