Here are a few books that speak to this topic to one degree or another from the perspective of the French Empire :

• A. Conklin, Mission to Civilize: The Republican Idea of Empire in France & West Africa, 1895-1930

• O. Abi-Mershed, Apostles of Modernity: Saint-Simonians & the Civilizing Mission in Algeria

• Daughton, J. P. An Empire Divided: Religion, Republicanism and the Making of French Colonialism, 1880-1914. Oxford: Oxford Univeristy Press, 2006.

I think one of the things you will notice if you read through these is that there is a great deal of tension between the desires of state administrators and missionaries-- they might cooperate at times, but they have very different ideas about what sort of colonial project they are engaged in. This is especially true in France where the ideological divide between Catholic (religious) and Secular (even atheist) administrators, officials, missionaries, settlers, investors, and merchants meant that there was often open competition between them. State administrators, did not necessarily even want missionaries to be present.

You may find that the 'true reason' for imperial expansion and governance varies between empires, colonies, and even administrators. It might be useful to look for common ground-- what made them think their projects would work, what sort of philosophies grounded their thinking.

You may want to look into the philosophy of the 'civilizing mission,' the idea that European empires had a moral and humanitarian obligation to expand-- and consider how it matches up against a 'christianizing mission.' While their end goals were not aligned, they were both based on the idea that colonial populations were missing something that justified European involvement or expansion.