Regarding French colonies, an overwhelming amount of which gained independence in around 1960, one source says there was a constitutional referendum in France in September 1958 and another source states September 1958 as the point when new leaders emerged in many of the colonies who would lead their respective colonies to independence in 1960.

I'll go do some reading and get back.

EDIT: So I may be mistaken but it seems that the 1958 Constitution was the first one to include guidelines for a legitimate referendum, which gave the colonies an opportunity to hold one regarding their status in the French community.

Someone better versed in the French system should probably take over.