Madame Defarge represents fate because she is knitting the names of future victims of the guillotine.
Madame Defarge is described in Book 2, Chapter 7 as a “woman who had stood conspicuous‚ knitting‚ still knitted on with the steadfastness of Fate.” Since Madame Defarge is heavily involved in the French Revolution, she is recording names of individuals she feels deserve to die once the revolution comes into being.
In Book 2, chapter 15, Madame Defarge’s knitting is described as disturbing.
It was additionally disconcerting to have madame knitting all the way there in a public conveyance.
When she is asked what she is doing, she replies that she is making shrouds. In other words, there is a connection between her knitting and death. She intends to be the decider for these individuals, and control their fate.
In Book 2, Chapter 16, the revolution has not begun yet, but the Marquis has been murdered, and Madame Defarge is “still knitting.” She comments to her husband that she has waited a long time for the revolution, so she can get her revenge on the nobles for what they did to her sister. Just killing the Marquis St. Evremone is not enough.
“It is a long time,” repeated his wife; “and when is it not a long time? Vengeance and retribution require a long time; it is the rule.”
“It does not take a long time to strike a man with Lightning,” said Defarge.
“How long,” demanded madame, composedly, “does it take to make and store the lightning? Tell me!” (Book 2, Chapter 16)
She continues knitting well past these chapters. For example, in Book 3, Chapter 3 she sets her sights on Lucie’s daughter:
“Is that his child?” said Madame Defarge, stopping in her work for the first time, and pointing her knitting-needle at little Lucie as if it were the finger of Fate.
Revenge extends to the children of the nobility. Even they cannot escape fate.