A few points:
A victorious Britain definitely could end up being in trouble in a near-future European war if victory causes them to overestimate their military prowess. Certainly in OTL their army didn't perform very well in the early phases of the French Revolutionary wars, and that was after a defeat that should have provoked more reforms. Their navy did a lot better, but it was facing a French navy that had been badly hurt by the revolution, supported by the fleets of reluctant allies. Against an unimpeded French royal navy, with more solid support from, say, Bourbon Spain, it could find itself in a similar situation to OTL's ARW - managing to hold its own, but not bringing the kind of decisive victories that it had during the 7 years' war.
Britain also has, like others have mentioned, the problem of having very few solid allies on the continent. That could change, of course, but British diplomacy, much like its military, was not performing that well at this period.
On the other hand, France would still be in tough shape financially, and even a successful war would probably leave it in even worse shape. This would put the same kind of pressure on the French king that Louis XVI was facing in 1788-89 in OTL. If the king is still Louis XVI, that's a serious problem right there, because Louis was just not an effective leader, especially not in a time of great domestic tension. Whether this would lead to something like OTL French Revolution beginning 5 or 10 years later is impossible to say. Louis or his advisors might still handle the situation better and achieve fiscal reform without losing their authority. If the estates-general is called in a time when the country hadn't experienced bad harvests and food shortages, as it had in 1788-89, there might not have been many food riots and uprisings in either the country or cities, which might have allowed the royal government to face down political opposition much more effectively.