I can't answer for every country, but as for Algeria, which was a french colony under Vichy's authority :

The american troops seem to have been very well received by the population. Lucien Adès, in his memoir about the war years in Algier, recalls scenes of euphoria in the streets, and a large number of young people trying to enlist to fight with the allies. He points to the fact that every segment of the population had reasons to rejoice : the french (who massively collaborated) felt that the fact that the American had negotiated with Vichy's general Darlan was a sign they were safe from repercussions ; the Jews could hope to see the end of terrible discrimination ; and the Arab population hoped the american would be favorable to decolonization.

That last part is the most significant. Indeed, the defeat of France in 1940, combined with the triumph of the american army a few years later, gave rise to many hopes of a liberation from colonial oppression. The Atlantic charter, with its emphasize on self-determination of the people, was mistaken by many as a sign that the american would try and break colonial rule. Ferhat Abbas, one of the leaders of Algeria nascent independence movement, had a photograph of Roosevelt in his pharmacy, and his Manifesto of the Algerian people was published just a few months after the liberation by the allies. So the arrival of the allies was a catalyst for a re-affirmation of the independence movement.

However, those hopes were to be dashed, most notably when the french population, in may of 1945, engaged in an incredibly brutal and violent massacre in Sétif and Guelma.

Sources

ADES, Lucien, L'Aventure algérienne, 1940-1944, Paris, Belfond, 1979

BOUCHENE & PEYROULOU, Histoire de l'Algérie coloniale, Paris, La découverte, 2012

PEYROULOU, Jean Pierre, Guelma, 1945, Paris, La découverte, 2009