Were military coups across Africa inevitable following decolonization? Were democracies in the French and British models doomed to fail?

It is somewhat difficult to make counterfactual statements about historical events as we cannot actually know for certain what would have happened had given conditions been different. What we do know, however, is that most African countries did not immediately and successfully transition to a form of western liberal democracy after the departure of colonial powers. 

A hidden assumption in this question that we should also note is that this question assumes democracy is somehow a natural end point of political evolution and that other forms of government are somehow failures. This may be a Eurocentric model of thinking about political systems. Chinese political philosophers, for example, would not agree with it. 

For democracy to become established, several forms of civic and technological infrastructure need to be in place. In Africa, many of the civic institutions were either weak or associated with the colonial powers. Even worse, democracy generally takes hold in societies that are somehow cohesive in ethnicity, language, culture, and religion. In Africa, many of the postcolonial "countries" were territories defined by lines drawn on maps by colonial administrators dividing up spheres of influence with little attention paid to such issues as tribal boundaries, meaning that the cohesive sense of "nation" was absent. Many civic institutions on which such a sense could have been established were either absent or distrusted as instruments of colonial power. Only a small group of elites, often educated in the colonial traditions, were literate or even familiar with large scale administrative skills and methods, and those elites were quite distant from the people they ruled in culture and lifestyle, having been to a large degree influenced and educated within European traditions. Even the physical infrastructure needed for voting was not in place.

The groups that led independence movements naturally tended to move into power at independence. There was no natural opposition or multiparty system. Instead, factions tended to be determined by tribal affiliation, and power seen as a way to control lucrative government largesse; there was little concept of rights of minorities. Thus even in countries that held elections, rather than engendering a sense of power sharing and minority rights, election results tended to confirm the exclusive grip on power of the largest faction that would use that power to benefit other members of their tribe. 

As Africa has developed an educated urban middle class, many countries (e.g. Kenya and Nigeria) have seen a democratic transition; educated urban professionals have weaker tribal affiliations and a greater amount of sophistication and power than people living in remote villages. This change, though, is relatively recent and was present in few countries at independence. Thus even when weak democratic structures were put in place by departing colonial powers, because they were imposed from above rather than rooted in local culture, they tended to evolve into authoritarian governments organized on tribal lines. 

Thus it does seem as though it was highly probably that democratization in postcolonial Africa would be a gradual and uncertain process.