In September 1958, all the French colonies which had not already achieved independence were allowed to vote on their future vis-a-vis the metropole, as part of the constitutional referendum on what eventually became the constitution of the Fifth Republic (the Fourth Republic collapsed in a putsch a few months earlier, driven mainly by the Algerian Crisis). Several (like French Polynesia and New Caledonia) chose to continue with their previous status, but most chose to join the newly formed French Community, which was supposed to be a Commonwealth type thing with autonomy but not independence (only Guinea went with independence in 1958). Some of these states (like Madagascar) had recent histories of rebellion against French colonial rule that were brutally suppressed, but others (like Senegal, Guinea, and I believe Mali) had much less combative relations. It's not an accident that the West African colonies had far different relationships with the Metropole than the North African colonies did, as France had a very different colonial policy there. There were fewer French people in general, fewer settlers especially, and, rather than suppressing local customs and religion, France tended to work with local religious leaders in West Africa (France thought of itself as puissance musulmane, a "Muslim power"). By the end of 1960, most of the states which had originally joined the French Community had peacefully transitioned to full independence (starting with Cameroun). This did not include Algeria, however, because France had tried to make Algeria not just a colony, but actually part of France (Algeria didn't gain independence until 1962). France had just given up the fight in most of its other colonies which meant that any state that transitioned during the 1958/1960 period and had not a bloody rebellion beforehand (mainly, but perhaps not exclusively, West African states) had a relatively amiable transition. The changes in colonial policy were being set in motion at least as early as 1956, though I am under the impression that they happened rather quicker than France expected (as the French Community was essentially defunct within five years).

Unfortunately, the little I know about this transition comes from knowing a little bit about French West Africa, not from knowing about France, so I don't know exactly how this decolonialization of the rest of French Africa relates to the Algerian Crisis of May 1958 and wider debates about the colonies happening France at the time, and I don't know whether it was debates over French Colonial policy in general, or merely Algerian policy particularly, that led to the collapse of the Fourth Republic and the reinstatement of De Gaulle in a semi-coup. But my impression is that letting Madagascar and all the West and Equatorial African states go peacefully was part of a strategy to keep Algeria as an integral part of France.

1960 was apparently known as "the Year of Africa" because of the large numbers of newly independent states, mainly from France (14 countries) but also the UK (Nigeria and Somalia) and Belgium (Congo).