The challenge could be done, but not after the stabilisation of the monarchy- which having Mirabeau not die would be a big help towards, he was chief propagandist for the crown and holder together of centrifugal things, he played a major role in keeping things from flying apart until 1791, getting the revolutionaries to compromise with the king and the king with the revolutionaries.
Once there is no countervailing impulse to the blood-struck Marat, the crown loses the propaganda war fairly quickly- or alternatively, reality reasserts itself.
What you need to get Napoleon and Davout on opposite sides- and Desaix should be in there somewhere, he was Davout's friend and patron until killed at Marengo- is for the Dantonist and the Robespierrist tendencies to fall out;
for the debate over the future of the revolution to reach boiling point before Louis' head comes off and the rest of Europe intervenes, so that there is enough external peace for the French to do something really stupid and fall out among themselves.
Danton was not a peaceful man; he gets a good reputation nowadays, as the moderate, constructive face of the revolution, but he was as intent on Louis' execution and the militarisation of the republic as anyone else, he was just less of a theoretical purist and more of a practical organiser. He was relatively sensible sounding, largely because he had to deal with confused, frightened people to get stuff done and there was no sense going around ranting and raving. He also had a sense of humour, which is relatively rare in revolutionaries but vital if you want to prevent a revolution becoming a bloodbath.
Robespierre, on the other hand, definitely put principle before human life. Suppose that they and their supporters fall out, massively, most of France takes sides, and things kick off from there. Who ends up on which side?
Davout was probably the more committed revolutionary- there is a story that may or may not have improved in the telling, of his regiment in 1790, he a junior captain, around the mess, a loyal toast was proposed- "Only an idiot could deny that the old system has made France great and led her to mastery in europe. Vive le Roi.'
Davout stood up- "Gentlemen, I am that idiot- Vive la Revolution." Unfortunately that may be the only joke he ever told. He is more likely to side with the sea green incorruptible than he would be with Danton.