Well, considering that an early absence of Louis XVIII and Charles X might cause too many butterflies among the Bourbon family, I'll sugest a different POD, and make them the sons of Charles die during the exile (let's assume they get some disease as happened in 1712). Now, assuming that everything until 1814 goes more or less like IOTL, considering the mess that would be the French succession going back to the Spanish Bourbons or the Orleans, could the Great Powers accept a different arrangement? I thought about three possibilities:
a) The daughter of Louis XVI, Marie Therese, IOTL married
Louis Antoine, Duke of Angoulême, son of Charles X and a heir to the French throne. Could after all the mess of Revolution and Napoleonic Rule just skip the Salic Law and accept the ITTL husband of Marie Therese as the new king, as a way of "revenge" the death of Louis XVI?
b) Considering that there is no clear Capetian successor, could the Habsburgs accept Napoleon II as the successor of his father, considering that his mother was a Habsburg herself?
c) Would it be possible that the Great Powers accept the formation of a French Parliament that would choose through an election the new king and the new dynasty of France?