My first question would be if they would have set up a monarchy in exile. And the effects of that on late 18th century Europe.
IOTL they both tried to escape dressed as common urbaners, but on their way to Germany(and then to Austria) they were recognised by a keeper of an inn in which they stayed as the king and queen, and were handed over to revolutionary authorities. They could have very easily escaped.
I wonder if a Louis XVI restoration would be a good thing. After all, he would've escaped from the revolution and lived all those years in exile. The 'restoration' of Louis XVIII, so to speak, gave the French a clean slate, if that makes any sense. I suppose after years of war under Napoleon/The Republic/Whomever (if we maintain a minimal butterfly net), the war-weary French would once again support Louis XVI. At least in the early 1770s, he was fairly popular. It was the economic policies of his ministers that really botched things, and Marie-Antoinette was simply a scape goat.
I know there's a myth of her being some hungry power behind the throne: not to deny that she didn't try to exert her influence, but Louis XVI had been scared to death by his Austrophobe tutor who instilled in him a fear of the House of Austria, and the 'domination' of the Habsburgs so that when Marie-Antoinette tried to intervene in the political arena, he shrugged her off and ignored her. Marie-Antoinettes power was limited to a brief period in 1790-1791 when Louis XVI was severely depressed: even then, she was just stamping his name onto papers which he wouldn't sign.