So, semi-successful Flight to Varennes, the royal family finds itself in England while the French have over-run or at least kicked the beejebus out of the Austrian Netherlands.
Leopold II is still going to issue his Padua Circular calling the European monarchs to help put down the French. However, ITTL, with the royal family in self-imposed exile, the National Constituent Assembly isn't going to declare the king to be inviolable. Now, I'm not entirely sure the assembly would decree a republic right then and there, after all the constitutional monarchy carried on IOTL until late 1792. However once the other German states start to dogpile in on the war effort, I don't think it'll take long for a republican government to come to fruition. That's not that big of a step really, as France had been essentially governed by the various Parisian committees and assemblies since 1789. We're probably going to see something like the National Convention take power. In this timeline the Declaration of Pillnitz is just a footnote in history, because Austria is already moving against France now that the royal family has fled, and Louis XVI is certainly going to be shouting out loud and clear 'kill them all.' So, France is run by an ad-hoc bureaucracy, fighting a war against Austria and the various German states. Sounds vaguely like IOTL so far. However we're likely to see something akin to the War in the Vendée much earlier, and much greater in scope. As well the extent of the radicalization of the revolution is likely to be even greater, as its seen that the royalty turned on the people, as opposed to the other way around IOTL. That's going to have a fairly large effect going onward. And let's not forget, the king is still alive in Britain. Any potential peace between France and the various European powers is going to depend on awful lot on how diplomatic Louis can be (which, luckily for the revolutionaries, isn't very much).