Not that there haven't been any number of other candidates mentioned, but I'd toss one more on the pile: Davout.
The Directorate was failing under its own greed and listlessness, and evolution to a more centralised, more militaristic government - the Consulate - was probably inevitable. But if you get a Consul with no dynastic ambitions, the Consulate can last a long time (that's one reason I like Davout: Massena probably would have tried to set his family up the same way Napoleon did, with similar results). After Austerlitz, not-Napoleon can literally wipe Austria off the map; guillotines on the Danube if he likes, cut it into a half dozen republics, even level Vienna and salt the earth. Napoleon did not do so because he was thinking ahead to his sons being accepted as a true Imperial House. A Consul who does that secures the Consulate, as Britain's only remaining possible partner is Russia, and Russia simply isn't invested enough in the West. Britain won't be "permitting" anything without somebody else to field an army for them.
The Consulate isn't probably what you or I think of as a Republic, but it could have been stable and durable, with a chance to democratize later.