The US is not 'taking'. Think of it as protective custody
Not entirely true. as Darlin told the US Ambassador in the Spring of 1942: 'If you come with three divisions we will fight you, if you come with twenty we will join you. Operation TORCH came with ten Allied division and the French split, some fighting the Allies, some swiftly joining them, and some disintegrating in confusion. Darlin received the direction from Petain that if the Allies did invade he was to negotiate with them rather than make a pointless & using fight. Unfortunately both sides botched the early negotiations.
Petains actions earlier in the year indicate he was thinking long term and saw the best case for France in a eventual Allied victory. Its unfortunate Admiral Leahey was not able to create a better condition ahead of it. My proposal for a Neutral US occupation of Neutral French colonies is towards the other limit of probability, but its still a goal to reach for.