Actually, there was a deal proposed for the exchange of French colonies overseas to the US in return for an extremely large (indefinite?) supply of aircraft early during the war (or perhaps before. I can't remember the exact date). It was a similar "colonies for aircraft" deal as "bases for destroyers" was, but would have proposed turning over the Pacific and Caribbean colonies as payment. France didn't really need the aircraft at the time, though, so the deal went nowhere.
So, with France considering the potential handover of colonies for just aircraft, they might be able to get a blanket supply from the US for at least some bases as concessions. If anything, the Free French government can basically use their presence as a pressure, noting that without some kind of support the French won't be able to continue fighting. So, some deal could be arranged.
And, well, if Japan has taken any more expansive moves, the US could be interested in securing the route to Australia, so New Caledonia and Polynesia would be useful, at least.