I understand why the Vichy government in Metropolitan France opposed the Allies (at least publicly) but why did French colonies like Madagascar fight back? They may have been legally bound to obey the legal government of France (the Vichy regime) but it was obviously a German puppet and the Allies+Free French were trying to defeat Germany and restore France, hardly malicious intent.
I may be wrong but it seems to me that various Vichy commanders just thought 'Yea the Vichy regime is just a Nazi stooge deporting Jews to death camps left, right and centre but we're gonna obey them anyway and fight against the people who want to see France free again'.
I just can't imagine British colonies/dominions doing the same if the UK was somehow conquered, I find the idea that Canada/Aus/NZ would obey a British puppet government and fight against the USA absurd.
What you have to understand is that the concept of "Vichy France" and "Free France" is an odd one.
So I will first adress the question of who was France, and then the question of why the colonies continued to fight.
Vichy France after all reasonable definitions was the actual successor to the Third Republic. Philippe Petain was legally elected Prime Minister after Prime Minister Reynaud had resigned in the fact of the ongoing German invasion and also the ongoing struggles and infights within his cabinet.
(the British had offered joint nationality to all French people, the so-called "Franco-British Union", should the French fleet be transfered into British control. While Reynaud himself was inclined to agree to the proposal, Petain and others were not, seeing it just as French subjugation by Britain rather than Germany, and thus not a viable alternative.)
So, Petain and his government were "France". Charles de Gaulle and his comrades in Britain, who on June 10th, 1940, called for continued resistance to Germany and then went on to form a government-in-exile and the later Provisional Government, were really just rebels, even though they at least had support from the Allied Powers.
The "Vichy Regime" would be continued to be acknowledged as a country and as the legitimate France by many neutral nations, including the USSR until Barbarossa began and the United States of America. (American governor to Vichy France and Fleet Admiral William D. Leahy is one of the more interesting characters of the United States Navy during the Second World War). Americans would end diplomatic relations with Vichy after the German operation "Fall Anton", which practically ended the independence of Vichy.
Now, next you ask why the colonies were loyal to Vichy France and not Free France. Again, "Free France" is a really hard concept that was legitimized by the fact that they would become France again after the D-Day invasions, but at the time, they were just no real alternative.
Even French Equatorial Africa, a major colony that (with the exception of Gabon) swore allegiance to the Free French Forces, was more of a self-governing associate than a "colony" of Free France, as the Free French government had no taxes they could raise and no resources they could produce with which they could help their colony grow and prosper.
And why did the Vichy Colonies fight the allies? Well, they were often not the instigators of such attacks. The allied Operation Torch into Vichy North Africa was literally a British-American invasion of a territory under control of a neutral country.
So, to sum up, instead of asking with our perfect hindsight why the Colonies supported Vichy, the real question should be why the colonies should not have supported them. The Vichy government was the rightful owner of all the colonies after international law, and the Free French Forces were really little more than a partially recognized rebellion.
By the way, your assumption that Vichy France was a German puppet is not entirely correct either. Petain and his crownies adopted most of their authoritarian reforms, including the changes to the constitution ending the Third Republic and even the antisemite policies, themselves, without viable historical sources pointing to major German involvement. However, to be fair, that also gave Vichy the ability to not directly take part in the Holocaust, which they did not themselves. (The Holocaust in France began mainly after Case Anton)
Sources:
Atkin, Nicholas: "Pétain", 1997
Breuer, William: "Operation Torch - The Allied Gamble to invade North Africa", 1985
Burrin, Philippe: "France Under the Germans: Collaboration and Compromise", 1998
Jäckel, Eberhard: " Frankreich in Hitlers Europa: die deutsche Frankreichpolitik im 2. Weltkrieg", 1966 (german)
Rousso, Henry: "Vichy-Frankreich unter deutscher Besatzung", 2009, (german)
Williams, Charles: "Petain: How the Hero of France Became a Convicted Traitor and Changed the Course of History", 2005
I hope it is okay to use Petain biographies as a source in this context. I studied that man quite a bit and thus know something about the conflict between him and De Gaulle and about what France was legitimate. (Mods? I at least read nothing against such sources in the rules.)