Jacobins aren't a political party, more like a mix of parlementarian club, think tank, and lobby.
By 1790, they clearly weren't most radicals, becoming so with the obvious failure of constitutional monarchy, and Louis fleeing to Varennes represented an important change in mentalities, a last drop, for what matters to the king and as well to the assembly (critically with the ludicrous official tale about the king being kidnapped).
Without Varennes, republicanism would have an harder time imposing itself and Louis remaining a token figurehead (which would cause some issues, see below); inner restrictions on movements would probably be delayed; and Feuillants holding more power and critically, no Champ de Mars massacre (it wasn't exactly Jacobins that began the whole thing) that radicalized Jacobins and decredibilized Feuillants.
It doesn't mean revolutionary violence would disappear but it would be turned to other focuses. (Note that revolutionary violence was widely accepted, with the situation going more radical. What was more challenged was the necessity of continuing it after existential threat vanished).
You'd have other clubs, tough. Cordeliers were significantly more popular and radical than Jacobins were, quite about a "watchman" role.
That said, having Louis XVI accepting revolutionnary changes would be really problematic : IOTL, while undecisive, he perfectly understood it was challenging his power and he didn't accepted that. You'd have to practically jail him in his palace, when simply getting rid of him would have been enough (maybe at the benefit of his son), but politically problematic.
The situation is going to be really tensed, and you'd still have revolutionary violence, from both radicalized clubs/parlementarian factions and governemental clubs/ministers (expect Champ de Mars massacre's equivalent to still happen).
Eventually, a revolutionary war is still likely to happen, especially with Louis XVI treated as a figurehead. Other crowned heads aren't going to be especially happy about it, and the likely failure of constitutionalist policies would, as IOTL, cause a large part of the Assembly to see in war the solution to political and economical problems (by marginalizing Jacobins, that were hostile to undergoing a war, it may be even more likely)