When the Third Reich annexed France, did France's colonies (in particular, Syria and Lebanon) go under German control?
French colonies remained under French sovereignty during the war - Vichy at first, Free French later - except in two territories: Tunisia, which was occupied by the Germans for 6 months after November 1942 (though it remained nominally a French protectorate), and Indochina, where the Vichyite government was overthrown by the Japanese in March 1945. Here is a brief recapitulation.
French Antilles and Guiana
French Antilles and Guiana were under the rule of Admiral Georges Robert. Robert had been appointed High Commissioner by the Republic in September 1939 and rallied Pétain in June 1940. He was a relatively faithful Vichyite, applying Vichy laws (including those against Freemasons and Jews) and the cult of Pétain, and organizing the repression against "subversive" elements, though this did not go further than jail sentences. Robert had a good relation with the Americans, and kept the islands and Guiana neutral. In April 1943, he refused Vichy's order to scuttle the fleet. Revolts in Guiana in March 1943 and in Martinique in June led to his ousting and replacement by Free French administrator Henri Hoppenot.
Indochina
Indochina was occupied by the Japanese, but they contented themselves with installing army bases and let the French rule its Indochinese territories (4 protectorates and a colony). Admiral Jean Decoux had been appointed Governor General of Indochina by Pétain immediately after the Armistice. Like Robert, he was a conservative favourable to Vichy who applied the laws and propaganda of the Pétain regime. He repressed opposition but more harshly than Robert: Communists and Gaullists were not only jailed, but tortured and killed. When it appeared that the Axis was losing the war, Decoux sent some signals to the Free French, causing the Japanese to oust him in a coup on 9 March 1945. An "independent" regime installed by the Japanese in Vietnam operated until 15 August 1945.
Subsaharan Africa
French West Africa (AOF) and French Equatorial Africa (AEF), along with African territories under French mandates (Togo and Cameroon) were placed on 25 June 1940 under the authority of a High commissioner, Pierre Boisson. Even though he was considered as left-wing and Republican, Boisson refused to deliver French Africa to de Gaulle. AEF and Cameroon nevertheless seceded and joined the Free French in August 1940, thanks to administrator Félix Eboué. In September 1940, Vichy troops in Dakar successfully repealed an attack by British and Free French Forces. Boisson, now a fully-fledged Vichyite, did like his colleagues Robert and Decoux: application of Vichy laws, Petainist cult and strong repression against dissidents. In November 1942, following the invasion of North Africa by Allied forces and that of the Occupied Zone in France by the Germans, Boisson rethought his loyalty to Vichy and switched sides, bringing AOF to the Allied. He kept ruling AOF until June 1943, when his forceful anti-Gaullism resulted in his ousting.
North Africa
French North Africa consisted in two protectorates (Tunisia and Morocco) and one French department, Algeria. In Morocco, General Charles Noguès was briefly tempted to join de Gaulle but rallied Pétain, who named him Resident. In Tunisia, Admiral Esteva, a Pétain loyalist, was also appointed Resident. In Algeria, Governors Admiral Abrial and later General Weygand ruled in the name of Vichy. All these men applied the Vichy laws, with a special emphasis on those targetting Jews. While Vichy's antisemitic laws had limited effects in the Caribbean, Indochina, and AOF, those laws were disastrous in North Africa, which had an ancient and large Jewish population. In Algeria, the Vichy authorities abolished the Crémieux decree of 1870, which had granted full French citizenship to Algerian Jews, and the Vichy authorities implemented discriminating policies (and forced labout in some case) in all three countries. From mid-November 1942 to early May 1943, Tunisia was occupied by German forces fighting the Allied advance in North Africa (Operation Torch), and the Nazis brutalized the 50,000 Tunisian jews, rackteering them, plundering their properties, sending about 4000 of them in labour camps, and occasionally killing them. Vichy rule ended in November 1942 in Algeria and Morocco (though Noguès remained Resident until June 1943), and in May 1943 in Tunisia, when the Allied drove out the Germans from North Africa.
Madagascar
Governor Armand Annet, another Petainist, was in charge of Madagascar in 1941 and 1942, and his troops fought a protracted war against the British invasion of the island (Operation Ironclad) between May and November 1942, with the assistance of Japanese submarines. Madagascar was put under Free French administration in December.
French Polynesia and New Caledonia
These territories joined the Free French between July and September 1940.
Syria and Lebanon
Syria and Lebanon were not French colonies, but under a League of Nations mandate assigned to France since 1923. They were never under German control, though German war planes participated in Syria-Lebanon campaign of June-July 1941 that opposed Vichy troops (led by High Commissioner of the Levant General Henri Dentz) to British, Australian and Free French ones.
With the exception of AEF and French Oceania, French colonies spent the first years of the war under Vichy rule, and their administrators usually implemented Vichy laws and spread the Petainist ideology of the Révolution Nationale, more or less adapted to local conditions. Many native children got to sing Maréchal nous voilà. Some of the administrators were true Petainist believers and loyalists. Others had a more flexible approach and switched sides, even managing to keep their position for a while under de Gaulle. Some administrators directly fought Allied forces, others were more neutral and only repressed dissidents. With the exception of Indochina, Vichy rule in the colonies was over by mid-1943.
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