Dickens chose to have Madame Defarge in his story, because such an evil character can make the story interesting, and makes the storyline to flow and makes the reader wander what he/she's going to do next and what happens to him/her ar the end of the story.
Madame Defarge is evil in her whole heart which, slowly, poisons her toughts too. She can't stand people such as Miss Manette, her father, and her husband. In her eyes they are against everything that is good and serves the future genarations. In the case of the French Revolution, lots of other people were killed and destroyed in such horrible ways, ways that only the worst of human creatures could think of. Actually Society should not accept people of this kind as people.
So Madame Defarge, and couple of her friends, wanted to destroy everybody like them. What's more they wanted to totally wipe out people like them.
Madame Defarge is a typical Dickens character, who wants to destroy everybody around him, who does not act as he pleases. Unless other stories, like Oliver Twist, A Tale of Two Cities ends in a sad way, but like his other stories, it gives a vivid and accurate picture of the age his writing about (in this case the French Revolution). Madame Defarge is lot like other characters of History that, leading lots of peoples, were the cause of innotient bloodshed and death.
Even though Madame Defarge's goal, to make the Republic organized, was a good thing, but she had gone too far. She didn't kill off just those who acted the wrong and sinful things, but most of the aristocrats of the time. Actually, it was her revenge, not only against those who hurt her, but other aristocrats too.
Such people, as Madame Defarge, were supported by a huge amount of people, because they said and tried to seem to be good, who has righteous goals, but inside they were hearthless, and unfotunately, lots of times, they won. Madame Defarge won most of her battles but lost the one in the book.