Except that Britain wasn't "fighting ostensibly to restore the French monarchy" until after the Convention executed Louis, and partly as a result thereof.
Fair point.
Okay, in that case, if a French state that doesn't execute Louis could have faced fewer enemies abroad (probable) the question becomes - is the Terror avoidable?
While there was a strand of opinion in Britain which held that any disorder in France was a good thing, there was also a strand of opinion that agreed with the Prussians and Austrians that this revolution was dangerous - over-extreme and incendiary. The more violent it becomes, the more viscerally terrifying it gets, and the more that tendency becomes heard.
It's hard to be sure, but I don't think Britain could have sat out the wars of the First Coalition once the extent of the Terror became apparent.
Of course, interesting butterfly if Britain does sit out, at least for a little while - the brilliant young Corsican Major of Artillery Napoleon Bonaparte maybe doesn't get to shine at Toulon. Could lead to his rising more slowly to power, or even being a General for another who made it first. (I think he was too talented not to go high, unless he were to be killed in an early action).