Ally is a very tricky word in this scenario, while Vichy did supply Germany with food and military supplies it was largely done in accordance to the Armistice. Outside of Vichy's own borders the government had little if no say in the actions of Germany, Italy, or Japan. The only ones that Vichy had a modicum of sway over was perhaps Germany and largely anytime they tried to sway Germany it was concerning a domestic issue ( supply shortages, blockades, telecommunications, removal of government officials, etc.) As far as I know however, when concerning colonies, Vichy only invested themselves in their North African colonies and islands of economic/military value such as Martinique. Ive only looked at Vichy through an American diplomatic lens so keep that in mind, I could have very well missed discussion or outrage on the capturing of these islands so keep searching!