Okay, well, I wrote this as a reply to a comment that was deleted while I wrote, so I hope it still helps with the OPs question.

The loss of life due to the French Revolution was of an order much greater than the American Revolution. For instance, the "Counter-Revolution" in the Vendee cost nearly 200,000 lives, over a quarter of which were casualties from military encounters, the rest from wholesale slaughter and executions (such as the infamous Noyades-- the whole event was even controversially labeled a genocide by Reynald Secher, a French historian, because of the state sponsored and highly regulated nature of some of the massacres). Not only was fighting in the Vendee particularly fierce during a period of the Revolution that saw numerous "Federalist" revolts-- that is regions outside of Paris that rejected the sort of nationalist project espoused by the Revolutionaries in Paris and preferred instead to keep their local autonomy, traditions, or influence-- but the French Revolution sparked an almost two decade span of continuous war.

Remember, other European powers did not sit tight and wait for the Revolution the wrap up and the Hapsburg's were keen to look out for the interests of their daughter/sister/cousin Marie Antoinette. HRE Leopold and Wilhelm of Prussia made clear their intentions to restore France to order with the Declaration of Pillnitz in Aug 1791 and when crowds seized the King in Aug. 1792 fearing he would flee the country, foreign armies crossed into France.

Its hard to peg down the true cost of the fighting the ensued, because there were numerous other conflicts connecting to it-- or precipitated by it-- the Revolution in Haiti, for example, unfolded in this chaotic context and benefited to some degree by the disorder the reigned in France and the generally anti-colonial/slavery sympathies of many revolutionaries (though Napoleon's rise sent the Revolution in Haiti into a new bloody phase).

The sheer spectacle of violence, as the now deleted one sentence answer pointed out, is also a big reason that the Revolution is remembered as especially violent. Heads on pikes, the scenes of Louis and Marie facing the guillotine, or the public dismemberment of Jacques de Flesselles, were all terribly disturbing images-- as was the seemingly unpredictable mob nature of much of that spectacular violence.