Why did they fight for their colonial masters?

There are a lot of reasons why, a few being:

Even though none of them would have been to the French mainland, they were French subjects and many would have felt a duty to the motherland in her time of need. In regards to the Algerians, Algeria had always been viewed as part of France, rather than a colony, so if France was at war Algeria was too. This status was the reason the French fought such a bloody war to try to keep hold of it in the late 50's early 60's.

To prove they were the equals of their colonial masters.

A chance to escape poverty and secure a new life in mainland France after the war for themselves & or their families.

To fight and protect their homelands from the racially motivated Nazis.

In India Ghandi and others like him were pro war as they belived once the war was won they would be given their independence by their colonial masters. I am sure many in French North Africa and French sub saharan Africa would have been of the same mind.