Why did Madame Defarge kill Charles Darney?

Madame Defarge does not actually kill Charles Darnay, who is replaced on the guillotine by Sydney Carton. But she hates Darnay because he is a member of the aristocratic St. Evrémonde family. Though Darnay has fled to England to escape his haughty aristocratic past, Defarge, an angry, bloodthirsty sans-culottes woman, becomes obsessed with his destruction.
It emerges that her hatred for Darnay is not born out of revolutionary zeal, but out of a terrible history between her family and the St. Evrémondes. The actions of some of Darnay's uncles directly contributed to the deaths of several Madame Defarge's family, including her sister and her father. So her hatred is not simply of aristocrats but of the bloodline of the St. Evrémondes themselves, and Darnay, as their living representative, becomes the target of her vengeance. She schemes to have him arrested and brought to trial, and she dies in the end attempting to murder Darnay's wife, Lucie, and their daughter. It is, then, out of revenge for past wrongs to her family by Darnay's estranged family that Madame Defarge schemes to have him executed. But the Darnay family escapes, as Carton selflessly goes to the guillotine in the end.