The "intro" answer is the aristocrats but it's problematic. For one thing, the concept of classes is sort of misapplied. The medieval/enlightenment era society in Europe consisted of estates, as the industrial revolution had not regimented everyone into a working class, or an organized class, or, what is the same, a soldier class. So the bourgeois, or merchant class, was in the same "estate" as everyone else in the Third Estate. The first estate was clergy, second was nobility, and Third was "everyone else."
At the outset of the 18th century France had inherited a lot of taxes and debts from English wars. The taxes were killing the peasantry, the third estate. There was no unified tax code, and taxes varied everywhere. There were arbitrary taxes on everything, such as road tolls, the "taille," and the corvee. The corvee was an indirect tax, since it was a requirement for forced labor that took farmers from their own land right when they were needed, in order to work the seigneur's land at harvest time. This is only a small part of the hardship the peasants faced. There were bread riots and even a "Flour War." So the aristocrats were the first to be in danger from the revolution.
However, the Red Terror is called a "Terror" because everyone was hunted and murdered. There is a death toll of some 20,000 people over the course of a year. So it's clear from the numbers that they were not all nobles. Those guillotines were going, ka-chunk, ka-chunk, 24/7. What happened is this.
Several aristocrats supported the popular uprising. The revolutionaries were genuinely sympathetic to the plight of the week and the poor and wanted to do something. Some, I'm sure, sides with the revolutionaries partly because they were smart enough to see the potential for increasing their own power, by eliminating the competition; and thus would have sided with the Jacobins out of self-preservation.
So you get these guys like Duc d'Orleans, Herbert Seychelles, and Saint-Just. When the rebels took control of the government, they formed a ruling body called the Committee of Public Safety, and there were just as many aristocrats as any one else on the committee, which numbered 12. These new rulers started seeing plots against freedom everywhere, and they became the worst threat to freedom themselves as they formed Revolutionary Army which terrorized the countryside. Euphemistically named "Representatives of the People," who were just members of the CPS, traveled to country town and village and mass-murdered people. The peasants hated them. They had killed the King in a Catholic country, so the peasants resisted them. To the peasants, they were terrorists and regicides who brought the full force of the state against them when all they wanted was to be free.
Lyons and the Vendemeer are conspicuous examples. One working-class member of the CPS, named Collot, went to Lyons and exacted personal revenge on the townspeople. The Vendemeer was a huge slaughter, and here, as in other places, the peasants were forced to live in the woods. Meanwhile, the Constitution was a joke. It's a famous phrase, "the Constitution is suspended until there is peace." Just a total sham.
Nobody was safe. They passed a law called 22 Prairial, which fast tracked executions: no due process, the trials were a sham, and accusation amounted to a death sentence. And some of these deaths were drownings. Families would be stripped naked, tied together, and pushed off boats in what we're called "Republican marriages."
Happy ending: Robespierre and another member of the CPS, Couthon, were upstairs in the palace called the Tuileries with Robespierre's brother, Augustin, when guards burst through the door to arrest them. They fully showed consciousness of guilt, too--as if mocking the people they were killing and mocking the idea of self rule by calling forced drownings "Republican marriages" didn't show it enough-- because they tried to escape. Couthon fell down the stairs. Augustin tried to jump out the window and was stopped. And Maximilien tried to shoot himself. It is not clear what happened, but a guard named Merdà shot at the same time, and one or the other bullets went into his jaw. The next day they all had nice gruesome, painful, degrading deaths at the guillotine.
