The men who come to arrest Darnay refuse to tell him why they are taking him, but when Doctor Manette demands to know, they tell him that Darnay has been denounced to the court at Saint Antoine by the Defarges and one other person. They won't say who that other person is.
In chapter 10, we find out who that third person is, and it comes as a shock. Doctor Manette had been called to treat a woman who had been raped by one of the St. Evremonde brothers. He is unable to help her, and she dies. The St. Evremondes had also killed the woman's brother, who had sought revenge for his sister. When Dr. Manette tried to reveal what had happened, the St. Evremonde brothers arrange for him to be arrested instead. Manette swore a curse on the whole family, wrote his story, and hid it in a hole in the chimney. The Defarges found it, and so Dr. Manette is the third denouncer.
Charles Darnay is the son of the elder St. Evremonde brother. He is being made to pay for a crime committed by his father.