The first thing that happened is that the Crown went bankrupt and its authority disappeared. The King needed to regain legitimacy and for that he needed to share power more broadly. France had a growing ambitious bourgeoisie who was largely shut off from power and wouldn't let this opportunity slip.

The King lost control of the reform process but he was still a convenient lynchpin of the Constitution, which still gave him extensive veto powers.

The French were the ones to declare war on Austria, it's interesting to think of an alt history where cooler heads prevail and focus on internal regime consolidation rather than chasing the reactionary émigré nobles.

It's still a very difficult environment for the Revolution, after all the Austrians might end up declaring war themselves anyway.

And if war does break out, it's dangerous even if successful, after all victorious generals create their own legitimacy.

In short, when state authority breaks down, things get confusing and mostly don't follow the plans of any of the actors involved.

IMHO limiting the power of the King was a good thing, and I think the whole would've turned out much better if France had managed to stay out of war for a while longer. But it would still have been a precarious regime.