I was quite surprised in finding out that during some overview reading , French Vichy colonies decided to support the new puppet government at the time and even fought against the Allies instead of helping them until liberation. So why did places like French controlled Madagascar which was very far away from any immediate Axis control battle against the Allies and not revolt?
It really comes back to the legal status of Vichy France - which in itself is quite complex.
After the French surrender the Germans occupied a large area of the north of France and the French coast, leaving a rump French state. But (despite the legitimacy of the Vichy government being disputed after the war) Vichy France was often seen and treated as an indepedant nation - recognised by the Canada, the US and USSR (among others) as the successor to the Third Republic.
Vichy France was neutral in the ongoing war between Germany and the UK, so British attacks on independent, neutral French colonies (such as Madagascar) were defended against.
And while there might have been some initial support to continue the war alongsode the British, there was an ever-present threat that if they didnt toe the line the Germans might invade what was left of France (this ended up happening in 1942 after the French colonies in North Africa didn't fight back against Operation Torch to any real extent).
Finally, the British had attacked the French fleet at Mers-el-Lebir in July 1940 (less than a month after the French surrender), killing 1,297 French sailors, so the French were not predisposed to throw in their lot with the British or their Free-French allies, even when the opportunity presented itself.
Not only did French Vichy colonies support the regime because of the legal status, it was recognized by the United States as the only legitimate state. The USA thought it could influence the Vichy state to a point, and like many allies, they underestimated how subservient to Germany the Pétain Laval government was.
On this topic, I recommend Our Vichy Gamble by William R. Langer
Vichy fought the Free French as well as the Allies. There was an incident in Syria where Free French and Vichy French fought each other, both believing they were the legitimate embodiment of France.
There is a even case where the American Government backed Vichy over the Free French : this was following the liberation of the islands of St Pierre and Miquelon on December 24th 1941 by Free French forces dispatched by General de Gaulle.
When the islands were liberated, Cordell Hull argued that the Free French - he referred to them as the 'so-called Free French' - should be expelled from the islands and the Vichy governor reinstated. This caused a minor kerfuffle between Washington, Ottawa and London. The main reason the Vichy regime was not reinstated was popular support for the Free French.
On this subject I recommend Seeds of Discord by Dorothy Shipley White as well as St Pierre & Miquelon Affaire of 1941 by Douglas Anglin.