Actually its currently a bit messed up.
Generally places like Cayenne, Tahiti and some of the french west indies remain "french" proper.
They get granted the entirety of the "old france" - so, often around 40 divisions of infantry and 40 odd ships - plus a few planes.
These , of course, are incapable of being supported by the IC income of those tiny couple of islands... but as the ai now "cheats" - they drop to zero org but dont die (ships, soldiers or planes). The French ALSO retain any expeditionary forces - so those british expeditionary forces also get stuck at zero-org but undying - and can be placed anywhere from tahiti to stuck on the uk mainland under "french" control... that control being able to do : absoltuely nothing at all as it has no income of ICs.
So its a double whammy - screws the french and hurts the english... resulting in lots of annoying units wandering about with zer0-org and all-but un-killable as they run away at the very first round of combat.
Now seeing as Vichy France, meanwhile, has zero of any troops of any type at all.....