France has only one citizenship, everyone holds the same French passport so everyone has the same freedom of movement within the EU.

It's not in Schengen, like most overseas territories in the EU, to limit illegal immigration into the EU (see Ceuta as well).

I don't thing the term "colony" holds. It is anachronic and refers to a system that no longer exists.

Ireland is not part of Schengen as well for example, it is because that is much harder to practically achieve for folks living on islands.

Guianans tend to get pissed off if outsiders suggest in any way that they are any different as a French region from l'Hexagone (the French mainland). Your banging on about colonies would not be well received there.