Remember how English monarchs kept their claim to the French throne after the 100 Years' War and kept it until, what, 1801? Your challenge, should you choose to accept it, is to turn that claim into reality by the present day with a POD no earlier than the death of Henry VIII.
Easy. During the French Revolution, the Royals are somehow prevented from escaping (border guards turning revolutionary?) and the whole Bourbon line is slaughtered at the guillotine by 1795.
After the Reaction, Napoleon rises, runs, and falls. In the postwar settlement, the powers decide to carve up France to prevent it from ever becoming a power again in its own right, maybe because Napoleon does more damage ITTL.
Aquitaine is made its own Kingdom, with a collateral Bourbon line ruling. Burgundy-Arelat is made a holding of the Savoys, in conjunction with Piedmont and Sardinia. Northern and Central France becomes directly administered by the British King as a separate dominion, like Hanover. George III becomes King of Great Britain and Ireland, of France, and of Hanover.