The question is difficult to answer for a number of reasons. First, colonial empires were never monolithic structures. Often, there was a great deal of agency granted to colonial governors who charted their own courses, leading colonies on very different paths. This is especially true in the case of France, where there was no colonial office to mirror that of the British Empire. Moreover, before the war, French governors were more inclined to grant greater power to colonial leaders, so long as they were supportive of the empire. Anticolonial movements, as can be seen in the Rif War of Morocco, were brutally suppressed. This question gains greater difficulty to answer, as there are questions about what Vichy even was. Some historians argue that Vichy was merely an authoritarian government that collaborated heavily with the Third Reich. Others argue that Vichy was a fascist state deeply influenced by Nazi Germany (although this interpretation is more or less discredited). The final view is that Vichy was a state that adopted a specifically French variant of fascism, rooted in peasant ideals and Roman Catholicism.

As you correctly mention, many of the French colonies supported the Vichy government, although many did not. For example, General Charles De Gaulle gave control of Chad to an anticolonial leader, Félix Eboué, after the Vichy-supporting leader of the territory (Pierre Boisson) was called to Dakar to act as High Commissioner of Colonies. French New Caledonia and its Polynesian territories both supported De Gaulle’s Free French from the start of the conflict. Others were instead on the edge, uncertain of which path they would take. French West Africa, initially leaning towards the Vichy government, was pushed deeper into Vichy control after the Free French bombarded Dakar, making it unclear that they were unable of taking back France or the majority of French colonies.

At the center of Vichy France’s ideological policy was the so-called “National Revolution,” which aimed to fight against multiparty democracy, elevate traditional values (traditional gender roles, for example), and oppose all concept of class conflict, which was gaining support in the French colonies under the guise of Marxism. As you may be aware, Vichy France supplanted the motto “Liberté, Egalité, Fraternité” with “Travail, Famille, Patrie.” Like in France, the Vichy government promoted national folklore, Christian symbolism, and utopians ideals of the French countryside. Here are some postage stamps from the period, showing the traditional nature of this symbolism. Special emphasis also went to discipline, both physically and mentally (although emphasizing the physical), with the French government initiating physical fitness projects and forming youth camps for the colonized. Here is a stamp showing that as well. This was also the case in France. In fact, the French policy towards the colonized mirrored that in metropolitan France that historian Eric Jennings goes so far to argue that Vichy “actually cloned itself overseas” (Jennings 2).

Interestingly, Vichy French policy had the opposite effect for the Vichy government than they had anticipated. Rather than colonial subjects truly adopting the customs that the Vichy government advocated for, they turned to anticolonial nationalism. During the Vichy government, indigenous customs were suppressed in favor of French attitudes and, as with water given a lid, the proverbial pot boiled over. To the dismay of the Vichy government, the Indochinese actually sided with the Japanese over the status of Indochina, assuming that they would be more likely to have rights and some semblance of autonomy under the guise of Japanese pan-Asianism, rather than European imperialism. As with Vichy, the Indochinese did not find this satisfactory either, leading the Vietnamese in particular to declare independence in September 1945. The particularist (and in many ways racist) language that the Vichy government used towards colonial subjects in all corners of the empire strengthened anti-colonial nationalism, culminated in the post-1945 independence movements and, eventually, decolonization in the 1950s and 1960s.

Lastly, I want to emphasize Algeria, as it was formally made up of three departments of metropolitan France. Here, fascistic attitudes long preceded the Vichy government, as settlers from France, Spain, Italy, etc. adopted an identity as “Latin” people with superiority over native Arabs. Although Jews had some rights in French Algeria, it was entirely impossible for Arab Muslims to gain citizenship without renouncing their religion. In Algeria, there was less contrast between conditions in the late Third Republic and Vichy than there was in other regions. This would later lead to the Algerian War, where paratroopers often re-embraced fascist ideals, sometimes going so far as to refer to themselves as “the Gestapo” when torturing those who fought against French rule and mocking republican values. This tragic war brought France to its knees, causing the dissolution of the Fourth Republic and nearly causing a civil war in the early Fifth Republic, when a fascist group of renegade officers created the “Organization of the Secret Army” (OAS), carrying out terrorist attacks both in France against French targets, as well as Algerian targets in Algeria.

The history of Vichy is still a sore spot in French historical memory, and is quite touchy. However, formerly colonized people view the Vichy period as a less distinct time in the past, although there were some clear differences. Instead, they saw often saw this a natural evolution of the associationist policies of the French colonial government during the late Third Republic (France, by and large, had discarded the “civilizing mission” after World War I, when they feared that the évolués, colonized subjects trained in French schools with the goal of becoming French citizens, were blurring the lines between “subject” and “citizen”).

I apologize for such a long-winded response, and hope that it was helpful. I know I did not include cases of every colonial territory and instead fixated on Indochina, but there is still a great deal to be written on the French colonies during the Vichy period, so there are many blank spots at the moment in this history.

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Sources

Alleg, Henri. The Question.

Césaire, Aimé. Discourse on Colonialism.

Conklin, Alice. A Mission to Civilize: The Republican Idea of Empire in France and West Africa, 1895-1930.

Conklin, Alice, et al. France and Its Empire Since 1870.

Cooper, Frederick, and Ann Laura Stoler. Tensions of Empire: Colonial Cultures in a Bourgeois World.

Fanon, Frantz. The Wretched of the Earth.

Jennings, Eric T. Vichy in the Tropics: Pétain's National Revolution in Madagascar, Guadeloupe, and Indochina, 1940-1944.

Kalman, Samuel. French Colonial Fascism: The Extreme Right in Algeria, 1919-1939.

Paxton, Robert O. Vichy France: Old Guard and New Order, 1940-1944.

Pollard, Miranda. Reign of Virtue: Mobilizing Gender in Vichy France.

Rousso, Henri. The Vichy Syndrome: History and Memory in France Since 1944.

Stovall, Tyler. Transnational France: The Modern History of a Universal Nation.

Thomas, Martin. The French Empire Between the Wars: Imperialism, Politics, and Society.