WI Louis XVI and Marie Antoinette dies before the Flight to Varennes?

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?
 
A disease would be best, I guess. It could conceivably take them both, without too much suspicions of murder.

Uh, considering the overall situation, accusations of poisoning and murder will fly no matter what. After all with Louis XVI dead, his son is now the perfect little puppet-king for the Revolutionaries to use.

And with his mother out of the picture, the traditional choice for a Regent is gone, so they are free to select whoever they wish.

This also gives more incentives to the Monarchists and European Powers to fight Revolutionary France even harder, now they have to rescue, "Poor, innocent Louis XVII" from the 'devilish' Revolutionaries who (maybe) murdered his parents.
 
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