I'm expecting Council to take over the Gallic core worlds and declare a Republique Gauloise with the crown now in exile. With no more homefront support the fleet in New London will likely retreat into now Aquitaine, Brittany and the Taus possibly sabotaging the lane network in Leeds. The situation for Charles would somewhat mirror Louis XVIII's "reign" in real life, claiming rule over Gallia but more than likely not officially recognized by most of the other Houses.
After that I can see a 3 way cold war in the Taus between Kusari and Bretonia over control of the Taus in general with Gallia staking claims on specific Tau systems such as 23 and parts of 53.