What if France stayed a monarchy after the trial and execution of citizen Louis Capet? And What if the young Dauphine, Louis XVII, was crowned King of the French? (BTW Marie-Antionette has to survive. Perhaps she had been the main witness for the persecution in the trial?)
Why does she have to survive? She was widely perceived as being the cause of the French state's money problems due to her personal spending and the fact she was Austrian didn't help.
And although she had a rather dignified exit (telling her son not to seek revenge, apparently), she was still trying to get the Austrians to intervene in the French Revolution even before it reached the "end the monarchy entirely" stage. Even if the Revolutionaries were willing to let bygones be bygones re: necklaces and dresses, she was basically committing treason there.
How would you let Louis XVII survive in any case? He reportedly died of scrofula that was probably, much like his mother's uterine cancer, exacerbated by his imprisonment.
You would need to avoid the entire Temple imprisonment altogether, which would mean the survival of not only Louis XVI, but also the archconservative Madame Elisabeth (she was apparently as conservative as the Comte d'Artois).
Also, the laws about a regency had been changed between the return of the royal family to Paris and Louis XVI's execution. Antoinette would not have been regent according to these laws, since the regency was vested in the senior prince of the blood, on condition of his being resident in France.
So, let's look at this. The Comte de Provence and the Comte d'Artois were already over the border; next prince du sang is noneother than Philippe Egalité, then his three sons, Chartres, Montpensier and Beaujolais (scarcely much older than Madame Royale herself). Then was the Prince de Condé (who was in his late 50s-early 60s, over the border), the Duc de Bourbon (roughly the same age as Egalité, over the border), and the Duc d'Enghien (over the border); and finally the Prince de Conti (born in 1734 and living in France).
Could turn interesting if Provence or Artois were to return to Paris to take up the regency.
What about butterflying the Flight to Varennes altogether? After all, that's what cost the Royal family all their credibility in the first place. As for the regency, well if the Émigré Princes were allowed to return and if they even wanted to return to ta revolutionary country, (those are two really big ifs) then the Comte de Provence would be the best bet. I mean his own reign in OTL wasn't half bad. U mean like he would be the most likely to compromise with the revolutionary's, other than Louis XVI himself.