Yes, they did. Remember, Marie Antoinette's brother was the Holy Roman Emperor and while originally many of the monarchies decided to wait out the Revolution to see what happened, when the rev. government declared war on Austria all bets were off. Austria-Prussian forces made up the First Coalition in the war against France (a war which France would win, which helped to solidify the Republic).

Specifically, the Duke of Brunswick issued the Brunswick manifesto, which essentially stated that if no harm was done to the Royal Family, the citizens of Paris would not be harmed, but if harm was done Paris would be burned to the ground. While ultimately it did more harm than good to the monarchy, it showed that lengths that the various powers in Europe would go to in order to protect their own.