With the American Revolution, the colonists established a Republic that limited the power of the government. In marked contrast, the French revolutionaries ended up with a socialist oligarchy that controlled the lives of the citizens and tried to keep them in a state of TERROR. The French "Republic" was not a true republic in the least.
Maximilien Robespierre: Justification of the Use of Terror
To understand "rule of law" in a Republic, one must under the distinction between natural law and political law. They are NOT the same! Natural Law refers to fixed standards of right and wrong. Political Law refers to laws chosen by politicians.
Political Law is often based on the whims of political correctness and the desire to get votes by enacting legislation to keep the majority happy.
Political Laws can - and often do - violate the principles of Natural Law.