Suppose that the Austrians kick butt early and do something like trick 300,000 (not a misprint, hundreds of thousands) conscripts into going into a trap (woods, pit traps, cannons, wall of musketballs, exploding boxes, something). So you have a "battle" that's really a massacre of hundreds of thousands of conscripts.
The Austrians then win several pitched battles (actual battles) and take areas in Burgundy, and secure the entire Mediterranean cost, while looting the cities. Then then give peasants they requisition material from script that says "to be redeemed (whatever currency Austria does) when the Monarchy of France is restored by its legitimate claimant" because... let's say they blame the cityfolk for the revolution.
Britain and Spain enter on Austria's side, causing the Directory to cave. Marie Anotnette and Marie Thérese of France are freed by their captors when they think they can get pardons for freeing them. Too bad they already guillotined Louis XVI and the sons died in captivity of something. Yay for Monarchy!
Oh, but there are no male descendants of Louis XIII of France left. Most of them are French nobles, so we can say they got caught by the rebels. Charles IV of Spain would obviously not be dead. OK, let's say either the Hapsburgs won the War of Spanish Succession or Charles IV died of Salmonella infection without a heir. My point being, no male decedents of Louis XIII left, not even in Spain, and not even through mistresses.
So... What do the three allies do now? Race to Paris and whoever gets there choses the new King? Or do you think they can agree on a claimant?
Would Maria Beatrice of Savoy work? She has good ancestry, Philip V of Spain, Charles Emmanuel III of Sardinia, Maria Theresa of Austria...
I don't know how the next claimant is going to be chosen.