I think there's a good argument that France got itself in that position as much because of poor policy and negotiations rather than because of their ideological positions alone.

Firstly some did give it a go to start a war with England if not on the same scale as the Wars of the Coalitions. Charles I was at this point Separately considered King of England, Scotland and Ireland and there were Scottish and Irish supporters of him whom after the first section of the English civil war fought alongside Royalists for Charles I then the II after his execution. Additionally there was some Spanish support. As part of the Anglo-Spanish War Spain did make an alliance with English Royalists while the protectorate made an alliance with France. This mostly involved some Naval engagements and the battle of the dunes where near Dunkirk where Charles II's royalists with Spanish support in the Spanish Netherlands fought English forces of the protectorate alongside the French and were defeated. If you've ever heard the folk song Dominion of the Sword that's what the

It batter’d their Gunkirk, And so it did their Spainkirk, That he is fled, and swears the devil Is in Dunkirk. stanza is referring to.

And while the protectorate also fought the Dutch for reasons entirely unrelated to their monarchy (Both were republics during this period, they fought primarily over marine navigation rights) a key difference here you'll notice is rather than having half of europe arrayed against it the English Protectorate has a few enemies and some allies. A lot of this is because the nature of the French policy in the years after the revolution did end up leaving it rather isolated.

Both the English and French monarchy had surviving members of the Royal family who fled the country, Charles II Charles the I's son to France first and then the Spanish Netherlands, and Louis XVIII and Charles X Louis XVII's brothers, to Savoy and then various parts of the Hapsburg's domains. France at this point had fought the seven years war against Britain and Prussia with Austrian support with the marriage of Louis XVII to the the sister of Leopold II of Austria Marie Antoinette. Leopold probably didn't want war with France but between the fact he suddenly died and was replaced by the more aggressive Francis and the aggressive demands the National Legislative Assembly made to attempt to make the Austrians return Louis and Charles to France. When Francis rejected these demands the National Legislative Assembly made Louis XVII declare war. Yes he was both still alive and still king at this point. Although after the attempted "Flight to Varennes" he had significantly less power.

So you can see here both how the popular imagination of how the wars of the coalition began is a little incomplete and here how specifically whom they declared war on left them isolated in Europe having just declared war on their most recent ally. Prussia being a major long term rival of Austria might have been an idea ally to court for a war with Austria as France had done in the War of Austrian Succession. But between disputes over the French owned territory of the HRE Alsace and the the Prussian declaration of support for the French monarchy that wasn't going to happen. So France's policies and aggressive rhetoric i'd argue played a major role in leaving it in such an isolated position.

Compare this and the Protectorate was perfectly happy to form alliances with monarchies and was less aggressive with the first country that Charles II attempted to gain aid from. As such they were in a much better position to form alliances with other powers, France and Spain having often recently fought in the 30 years war France at this time made a natural ally of the protectorate. While England could have probably avoided the Anglo-Dutch war during this period its diplomatic efforts were far more successful at avoiding the isolated position of France.

But the 30 years war itself is another reason. Additionally people who may have chosen to get involved on the continent may have been significantly less likely to do so on account of having recently had to fighting this massive conflict. England being not that politically important at this time. And so other than the other crowns which Charles had held and Spain few supported Charles II in no small part because the HRE in particular was tired of conflict in recent years and England wasn't important enough to be worth spending significant resources over in the eyes of many.