Carlo's Decision to Switch Sides

The most cynical reading of this decision is that he'd only stuck by Paoli to advance his own interests. Carlo certainly had a strong impulse to pursue his own self-interest, so I wouldn't call this narrative out of character. The really advantageous time to switch sides would have been soon after the French arrived. Being part of a French Corsica might not have been Carlo's first choice but if the only other alternative was obscurity and irrelevance in London, Carlo chose to deal with France.