Nope; I would say it was not clearly defined, but instead a vague notion that subject peoples could be 'civilized' or tutored along a linear progressive path towards being more French. There is tons of great work that had been done on this topic in Africa and across the colonial empire. Generally the civilizing mission- and its related white man's burden- were ambiguous paternalistic notions of what the empire was trying to accomplish and what it naturally would accomplish. Civilization was ideally brought to subject peoples through education, morality, art, science, and health. Just how these were imparted on people was never quite agreed upon and varied wildly between colonies and administrators. Some, relied heavily on missionaries and church infrastructure to expand education and especially Catholicism as something essential to French identity; but in the late nineteenth century- really the hey day of the civilizing mission, though it had earlier incarnations, French identity was and is still very much contested by those who see it as inherently secular, an idea from the French Revolution, and those who see it as necessarily Catholic. In the colonies and in the vein of the civilizing mission this played out in either support or opposition to the church; whether or not it was funded or subsidized by the state or put in competition with secular education. The civilizing mission was among other things also a conscious effort to differentiate themselves against the British colonialism in the Americas and Australia. As Abi-Mershed explains, "Assimilation was conceived as a plausible means to reconcile the fact of colonial rule with the revolutionary slogans of human emancipation and individual equality."

The civilizing mission and its accompanying policy of assimilation, the belief that subject peoples could become French had appealed to the French love and belief in universal qualities- order, equality, brotherhood, and the belief in the greatness/benefice of French culture. By the beginning of the 20th/c this view was seen as dangerous, unscientific, harmful and largely replaced by a policy of association that stressed flexibility to local circumstance, respect for native institutions, and claimed to engender greater native cooperation and participation. The 1890s saw the beginning of a turn away from assimilation- there was growing pressure to monetize the colonies and follow the lead and methods of other great colonial powers like the Dutch and the British- both of whom managed to use small European bureaucracies to rule over great, profitable overseas empires. As Raymond Betts offers, "British and Dutch colonial prosperity was thought to be the result of a sound native policy which necessitated the retention of native institutions, or, at least their façade." Furthermore, the collapse of the Spanish Empire was seen as proof of the folly of assimilating a people who would bear you no loyalty and see themselves as equal.

So rather than 'assimilation' as the goal of the civilizing mission, policy makers and government officials turned moved to the idea of 'association.' Association paternalistically assumed that French culture and material wealth was harmful to native peoples until they advanced more and operated under the assumption that France conquered because man is naturally aggressive and bellicose- not humanitarian. This is very much in line Atavism and the idea that some societies had reached points of stasis and could not be forcibly advanced through some civilizing mission; that the civilizing mission itself might be dangerous to these peoples- corrupting them or literally killing them thanks to the ensuing depression and nostalgia they would feel. Association was sold as akin to fraternity (but not equality); as “assistance” for economic development rather than exploitation. It was a new version of the civilizing mission concerned more with material and economic development and gradual cultural change.

Did Africans buy into it? I suppose it depends. Certainly there were people who took advantage of what the Civilizing Mission had to offer in terms of education and advancement- yet there was a glass ceiling for subject peoples, there were severe limits as to just how far you could be assimilated or allowed to advance. For the most part the civilizing mission and its sort of gentler- though no less insidious paternalism- didn't last much longer that the 1840's-90's, the time frame when France rebuilt its colonial empire- so most colonies were not long governed under that ideal.

Some great reading on this topic; the first one is a classic IMO, the others more recent work specific to Africa.

• Betts, Raymond F. Assimilation and Association in French Colonial Theory 1890-1914. New York: Columbia University Press, 1961.

• Abi-Mershed, Osama. Apostles of Modernity: Saint-Simonians and the Civilizing Mission in Algeria. Stanford: Stanford University Press, 2010.

• Brower, Benjamin. A Desert Named Peace: The Violence of France's Empire in the Algerian Sahara 1844-1902. New York: Columbia University Press, 2009.

• Conklin, Alice. Mission to Civilize: The Republican Idea of Empire in France and West Africa. Stanford: Stanford University Press, 1997.