I suppose the revolution could avoid involving any of the outside powers. But to do that you are probably going to get a revolution nothing like the one we knew from OTL. The key is to keep the moderates, who ran the opening stages IOTL, in control. If they can force through some form of constitutional monarchy and keep the radicals out (and keep the king from running or otherwise mucking things up), then it is possible that you could keep the other powers out of France.
However, this will drastically change the pattern of European history. The most obvious effect is no revolutionary wars, and thus probably no Napoleon (he may rise to prominence, but never near the heights he reached IOTL). This will probably embolden less radical revolutionaries elsewhere, so we may see other revolutions crop up elsewhere, possibly leading to a repeat of the French revolution in some form (in Prussia, say). Otherwise, for the moment, borders and culture to some degree get temporarily frozen where they were before the French revolution (for instance, Austrian netherlands). And many ideas and people who rose to power in the wars of the subsequent decades will not come around. From a military standpoint, things like the levee en masse and the corps system will not be adopted, because they were developed or popularized during the wars of the revolution or the napoleonic years.