Well, unlike the prior Reign of Terror, a "Night of the Long Knives" would swiftly wipe out the organization and leadership of the conservatives/monarchists after a night, even Thiers could be killed. You can look at the way the Conservative Right essentially disappeared in the Third Republic until the 1930s. This purge could look like a successful Gunpowder Plot, lets say: Conservatives and Monarchists hold an all-party meeting at a big building. Suddenly, the building blows up (original Gunpowder Plot)/Suddenly, Republican guards locks the doors of the building and burn it down. Both are very quick and swift.
There would be no intervention because other countries were also undergoing revolutions at that time.
First of all there were no liberal paramilitary groups ("Republican guard") to carry out such a plot.
Secondly, there would be no gathering of all conservative forces mainly because they were not a unified group, there were for example monarchists but they were split in three different groups based on who they supported and consequently did not get along with each other at all. You will never find the legitimists, orleanists and bonapartist holding a joint meeting.
Third, the conservative right did not disappear in the third Republic. You may want to read about Raymond Poincare, Georges Boulanger, to learn about some conservative politicians or the Conservative Union, the Ralliement (a catholic conservative party), the Progressive Party (names can be deceiving) to familiarise you with some movements.
Fourth, not all other countries were undergoing revolutions, Spain and Britain for example did not. And if the revolutions start to look like a repeat of the French revolution they might well intervene against them. Russia also saw no revolution of its own, and if the French start to murder the nobility, the Prussian and Austrian might well invite them to protect themselves.
Finally if we disregard all of that and assume for the moment that the liberal revolutionaries somehow manage to successfully murder all conservatives, I don't see why the won't use the same tactics against the radical . If you are willing to kill all opponents to the right why would you try to negotiate with your opponents to the left and adopt their policies?