They were already at war and they failed. The popular imagination of the French revolution gets very condensed timewise where in reality the French revolution was a mixture of a drawn out process over the course of several years marked by occasional points where tensions rose to a breaking point resulting in explosions of violence.

Since Women's March on Versailles in 1789 Louis had been forced to live in Paris rather than Versailles, at this point the kind was basically well within reach from the Parisian revolutionaries which obviously meant he had to pick the policies and positions he expressed careful given that he lacked sufficient support from the army outside of some units like the Swiss Guard within the Maison du Roi to be able to prevent the Parisians from storming his home should enough of them commit to it. As tensions continued to mount over the next couple of years Louis attempted to flee France in June 1791, this failed and they were taken back to Paris with much of Louis' power being begun to be stripped from him shortly after in an official capacity. Now Leopold II who was the Holy Roman Emperor and Archduke of Austria among other things who was Marie Antoinette's brother was a little reluctant to go to war if he could help it but in response to that a little after this incident along with Frederick William II of Prussia declared their support for Louis. Over the course of that autumn rising tensions between the French National Constituent Assembly and the Prussians and Austrians among others lead to relations deteriorating as the two sides exchanged threats over topics like the power of Louis and the status of nobles (such as the king's brothers) who had fled France and were trying to raise forces and funds to march back to France and fight the revolutionaries.

This cumulated in April 1792 with the National Legislative Assembly (because the revolutionaries were changing the name of their government a lot) declaring war on the crowns of Austria and Prussia. Over the spring and summer of that year there was extensive fighting. The Austrians primarily found themselves forced on the defence as the French attacked into the Austrian Netherlands, modern Belgium. Meanwhile a Prussian lead force attempted to go on the offensive further south initially making some headway but while advancing on Paris during some absolutely horrible weather the Prussian force faced off against a new army the French had raised at Valmy and the Prussian commander decided after a brief artillery duel that he'd rather not fight this battle and withdrew. Some more limited fighting continued into the Autumn and in places like the Vendee a guerrilla war against counter revolutionary royalists began.

The fact that troops nominally fighting on the Louis' behalf seriously damaged any remaining loyalty to the monarchy much of the more moderate members of the National Legislative Assembly might have had for the monarchy (the National Legislative Assembly was on the whole more moderate and middle class than most of the street fighter Sans-culottes) and their willingness to accept a constitutional monarchy weakened. Thus it was after a season of campaigning with the Austrians and Prussians that in early 1793 the king was executed with Austrian attempts to retake France having failed.