I cannot answer your question to full extent, what I do know is that Stalin expressed the following concerns to the French Communist Party regarding continuing with the communist revolution orientated policies:
"Le camarade Staline explique qu'il a abordé cette question parce qu'il lui semble que les communistes n'ont pas encore compris que la situation a changé en France. Les communistes n'en tiennent aucun compte et continuent à suivre l'ancienne ligne alors que la situation a changé. [...] La situation est différente, nouvelle, favorable à de Gaulle [...] et il faut opérer un tournant. Le PC n'est pas assez fort pour pouvoir frapper le gouvernement à sa tête".
It means that Stalin explained to them that he was not in favor anymore (!!) of such an idea because the French Communists did not understand that the situation in France had changed. He explained it as a situation most favorable to De Gaulle. The French Communist Party would not be strong enough to defeat a government with him as leader.
The reasons why Moscow made this statement towards the French are various, we can take it literally, another reason suggested by other historians [not Buton] was that Stalin did not want to make too much trouble with the Americans [and the Allies in general] at that moment, Russia was winning but suffered heavy losses. Another strong theory was that the dissolution of the Komintern (the organization that advocated World Communism) in 1943 made the Russians worried with including the French Party that it would become highly inflexible leading to problems in both countries. However Buton himself states that Moscow was never dependent on the French Communist party for such an argument and the reason can be most likely found in the quote or statement above wherein he favored De Gaulle at that point and it was a choice of strategic interest serving more the Soviet direct needs. Maybe you can see it as an expression of Realpolitik.
A strong argument for Buton's point is that De Gaulle visited Stalin in the Autumn of 1944 after which he proclaimed:
"Ne vous fâchez pas de mon indiscrétion ! Je me permets seulement de vous dire que je connais Thorez et, qu’à mon avis, il est un bon Français. Si j’étais à votre place, je ne le mettrais pas en prison. Du moins, pas tout de suite ! » — « Le gouvernement français, répondis-je, traite les Français d’après les services qu’il attend d’eux."
He says in the above quote more or less that Maurize Thorez, the leader of the French Communist Party, is a Good Frenchman, De Gaulle knows him and sees him as a friend, it is a clear sign of support. The reader should take into account that Thorez was tried in absentia and sentenced to death when he did not fight Germany during the invasion but chose to desert and flee to the Soviet Union, he was pardoned by De Gaulle, an important step for both Maurice Thorez and the French Communist Party because this was for them an important base to work together with Charles De Gaulle from 1944, and Thorez himself even became a vice premier of France.
The same reason he discouraged revolutions and independent Communist movements all over the world and why the two actual revolutions (As opposed to the take-over of the governments under the auspices of the Red Army), happened outside his knowledge, help, and consent, China and Yugoslavia. In fact he discouraged the Greek Communists during their civil war because he had agreed to give Greek influence to Britain. And therein lies the core of Stalin's thinking.
Stalin's chief concern was the security and power of the USSR. While he believed that socialism would eventually overtake capitalism, he felt he needed to shore up and maintain Socialism in One Country, and that revolutions which endangered that security, including relations with the West, should not be undertaken. His preferred government in all post-war territories was a broad anti-fascist coalition, including Communists, non-revolutionary Socialists, Liberals, and Conservatives, and until the hardening of the Cold War that's what was put into place. Stalin was interested in security and development at home above all, not in attempting to export the revolution all over the world like Trotsky.
Anyone looking to learn more has a wide range of sources at their disposal, but I personally love to recommend Eric Hobsbawm every change I get, so I will recommend Hobsbawm's Age of Catastrophe, 1914-1991, the fourth entry in his Age of series.