Just before we start, your question implies that Germany regularly took control of French colonies after their victory in 1940. Absolutely not. Not a single German soldier stepped foot on the soil of French Guiana, French Equatorial Africa, French Indochina or French Polynesia. The Germans neither had the means nor the interest to sustain a colonial occupation. The only colony that comes to mind that ever even saw German forces was French Tunisia, and that one for somewhat unrelated reasons.

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French Guiana had quite a bit of drama during World War II, but it was resolved mostly without armed struggle.

You see, all French colonies had a choice to make: Either you stay with Philippe Pétain and his Vichy government (by all reasonable standards the proper government of France) or you seek allegiance with the rebels under the leadership of Charles de Gaulle.

Now, there are plenty of good reasons to choose Pétain, from "not being at war" to "not betraying the legitimate government of France", but even back then, the Vichy government proved too weak to reject Japan's request for military access to the Tonkin region in French Indochina [contemporary northern Vietnam] in September of 1940, leading to Indochina effectively becoming a Japanese springboard in the war against the Republic of China.

But alas, even though there was quite a bit of pro-rebel sentiment in French Guiana, governor Robert Paul Chot-Plassot (in office between 1938 and 1942) decided to remain in the government line and stayed loyal to Pétain. The same held true for René Veber's second term (making Veber both Chot-Plassot direct predecessor and direct successor), remaining pro-Vichy exactly until March 18th, 1943, when Veber was succeeded by one Jean Alexandre Léon Rapenne.

Jean Rapenne was one of the colonial administrators loyal to the rebels, making 18 March 1943 the definitive date when the colony of French Guiana [called French Guiana and Inini at the time] switched sides to the rebels, who from 6 June 1944 forward would increasingly become the real France.

So all that colonial political intrigue is already quite Game of Colonies-y, but the most interesting part about the person of Jean Rapenne to me is that he was part of a greater political struggle within the French rebellion, as he had been the favorite of Henri Giraud and his hyper-reactionaries, whereas the (in comparison) more liberal Charles de Gaulle had preferred one Maurice Bertaut. Henri Giraud had a good outlook on being French leader after the war, until he didn't tell the French national committee for liberation about how he armed thousands of radical communists in Corsica's "Front National" with allied weaponry. Oops. And then he kind of got busted for having amicable contacts with former Vichy secret service agents that had mercilessly persecuted the French resistance. Double oops.

The "De Gaulle vs Giraud" narrative is in itself part of a greater story ark, "United States vs United Kingdom". You see, President Franklin Roosevelt [USA] had been quite friendly to Vichy government officials and advocated that Vichy personnel should be graciously reintroduced into the allied apparatus, whereas Winston Churchill [UK] was more friendly to Charles de Gaulle (even though the two were said to personally be adversaries more often than not, again, more drama) and despised the Vichy regime. Churchill believed that those Frenchmen part of the rebellion should be rewarded, and those part of the puppet government ignored if not punished.

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Alright, I am driving a bit off topic here. I am merely providing a bit of greater context, as the question in itself is quite short, if you will.

I am open to any further questions.

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Sources and Further Reading:

• Dirks, Carl: Der Krieg der Generäle. (1999)

• Rousso, Henry: Vichy: Frankreich unter deutscher Besatzung 1940-1944. (2009)

• Piekalkiewicz, Janusz: Der Zweite Weltkrieg. (1985)

• Piekalkiewicz, Janusz: Schweiz 39-45. Krieg in einem neutralen Land. (1978)

• Tobler, Hans W. et al.: Handbuch der Geschichte Lateinamerikas: Lateinamerika im 20. Jahrhundert (1996)

• Zentner, Christian: Der Zweite Weltkrieg. (1981)