The Flight to Varennes, and the Brunswick Manifesto that followed, could arguably be said to have been the death blow that killed any hope of a surviving monarchy in France: it persuaded the common Parisien that the King was a traitor to the nation, in league with the foreign kings and the émigrés. The decision to flee was largely Marie Antoinette's.
But if Louis XVI and Marie Antoinette dies some days before, the king of France would then be Louis XVII, only 6 years old at the time.
Who would have been the regent then? That man would have the fate of France in his hands. If he is in favor of a constitutional monarchy, then we could see a king working with the Assemblée, rather than against it. This would also butterfly away the War of the First Coalition. Many of the causes of instability of the early revolutionnary period would disappear as a result...
So, whio would be the likeliest candidate for Regency? Could the leading politicians of the time influence the choice in any way? And what would be the consequences?