In 1958, most of France's African colonies voted to maintain their close association with France in the Communauté française instead of choosing independence. Only two years later, all of them became independent. What happened to cause this sudden change?

This is complicated. You have to remember first off that the 1958 vote was on the new French Constitution that formed the Fifth Republic, with the French Community being only one part of what was being voted upon. In the case of the African territories, the 1958 vote followed on the 1956 Loi-cadre reform that transferred considerable powers of sovereign administration to French colonies as well as establishing universal suffrage.

One African territory voted no in 1958 (Guinea) and was granted immediate independence (which the new French government did its best to implement in the most sullen and resentful way possible). That was the first blow against the association proposed in the 1958 vote. The more significant blows between 1958 and 1960 were the war in French Indochina and the war in Algeria. Along with Guinea's "no" vote and some agitation in many Francophone territories to allow each territory to control its own internal political structure, these developments led to a 1960 amendment of the Fifth Republic's constitution that allowed territories in the French Community to write constitutions and in effect become independent. At this point, all the Francophone African territories did so (though I'm not even going to try and get into the additional complication that several former French colonies in Africa were actually UN-controlled and subject to a different administrative regime on paper).

But this too is a bit misleading, as all of the Francophone West African territories except Guinea retained some of the hallmark features of the French Community, most notably a regional currency that was tied to the French franc. Many of the characteristic institutions of the French Community retained considerable strength in Francophone Africa (such as French-subsidized libraries and French-language education). Moreover, France frequently engaged in military interventions in Francophone Africa up to the controversy over France's role in Rwandan politics and the genocide between 1990 and 1994, often invoking the idea of a "Francophone Africa" that was still a distinct geopolitical unit or entity.

The basic upshot: the French Community created in the 1958 Constitution was not the diametric opposite of the independences declared in 1960; most Francophone African states retained many of the key features of the French Community and remained tied to France in a number of ways that were quite different than those existing in the British Commonwealth.