The flaw is inherent in the design

Not that dead horse again

It is massively dishonest to compare early years of the French and US republics and state the differences were caused by their respective constitutions. The French republic had to contend with multiple hostile vultures (neighbours) all too happy to intervene military, profit from the political upheaval, and settle centuries-old scores (aggravated by European nobility cross-continent alliances and intervention by religious authorities). And in case that was not sufficient, don't forget the revolution started in the first place because people were starved after several years of bad harvests combined with economic crash.

The USA OTOH had help from every English enemy and was an ocean away from its main opponent anyway.

In other circumstances there would have been little blood-letting in France. The king was even unharmed and left in place at first, it took his fleeing abroad (with the intention to return at the head of a foreign army) to radicalise the country.

The same repeated foreign interventions, religious meddling and nobility plotting caused years of bloody religious wars in France a few centuries before, with no revolution involved. It was endemic in Italy for a long time.

So don't get fooled by the anti-Napoleonic propaganda that lingers in the anglo-saxon world. The horrors that occurred in Europe at the end of the 18th century had little to do with political systems and can be explained 120% by the usual clashes between powers with too much influence/wealth/armament/ambition and too little sense.