Complex sentence: In the "mixed" communes, where Muslims were a large majority, government was by appointed and some elected officials, including representatives of the grands chefs (great chieftains) and a French administrator.
Split into simpler sentences: In the "mixed" communes, where Muslims were a large majority, government was exercised by officials, most of whom were appointed but some of whom were elected. These governments included representatives of the "grands chefs" (great chieftains) and a French administrator.