The wikipedia article for Vichy France has a pretty good map, a low-res version of which I'll put here:
The map shows which territories were originally Vichy, and when they changed to Free French control (except for the yellow states in Southeast Asia, which came under Japanese control).
However, it's missing two French Territories: Saint Martin and Saint Barthélemy. The two skyblue islands you see in the Caribbean are actually Guadeloupe and Martinique.
I would like to know if Saint Martin (the French possession, not the whole island) and Saint Barthelemy were originally under Vichy control, and when they came under Free France control. Who was governing them at the time and what statements did they make after 1940 June?