... the Federalists and Lyon revolts were literally reactionary, though.
I mean... no? They erupted in response to the purge of the Girondins, which wasn't very revolutionary. Unless you define the revolution to mean Paris, fighting against authoritarian centralisation of power seems very in line with the Revolution even if the leadership of the revolts did tend to have conservative sympathties.
to the point of rallying a continent-wide coalition to reinstall them as well as a civil war to help them along?
That's... uh... wow. You should revisit the French Revolution and surrounding wars, seriously. For reference, though, the civil war was based in pretty legitimate grievances against Paris authoritarian overreach, the purge of the Girondins for the Federalists and religious oppression+conscription for the Vandee folks. As for the Revolutionary wars, France literally declared war first; everyone else wanted it to collapse in silence so they could focus on Poland. Neither of these were significantly affected by the aristocratic sour grapes.