I’d question the premise a little: the monarchs of Europe were actually somewhat slow to react to the French Revolution (in part because it came at a time when France had been a major hegemonic power in Europe that everyone else was trying to contain), and were kind of waiting for the thing to collapse from the inside until the Girondins decided to pre-empt what they saw as a monarchist/Austrian plot against the Republic (and to give themselves a political edge against the Mountain by emphasizing military patriotism vs. further republican levelling) by going to war with everyone, and then when they realized that A. the French Republic could kick their ass, and B. their own subjects might be interested in this whole republic thing, they realized they were in an existential conflict and settled in to fight it out to the end.
Whereas with the English Civil War, you had a very different European context. The religious wars in France, Germany, etc. and the
big geostrategic conflict between France, the Hapsburgs, and the Ottomans
were the main centers of attention. To the extent that there was international involvement/interest in the English Civil War, it had to do with that conflict would affect the other – was England going to side with Catholic France against Protestant Holland or vice versa? Another big difference is that the English Republic wasn’t that evangelical in either sense – the Republic didn’t try to promote republican uprisings in Europe, and didn’t engage in foreign policy on Protestant terms. They went to war with Protestant Holland over trade, and they went to war with Spain (allying with Louis XIV! talk about strange bedfellows) to get their hands on Spanish commercial colonies in the Caribbean, not because of Spain’s Catholicism.