Chapter XV of Book the Second of A Tale of Two Cities finds the mender of roads escorted into the wineshop by Ernest Defarge and introduced to Madame Defarge. In the wineshop, there there has been more than ordinary drinking, and drinking of a sour wine. Defarge introduces the blue-capped mender of roads as "Jacques," and he relates what he has seen on the road. He has seen the Marquis's carriage pass by with a man hanging onto the bottom of the carriage. This man had escaped when the Marquis called for him, but he has been "unluckily" found. The guards force him along as he is bound and has become lame. When he falls the guards laugh; all the village whispers by the fountain.
As the mender of roads passes the prison, he sees the man; he regards the mender "like a dead man." As Defarge and the other Jacques listen, they assume the air of a tribunal as the mender continues. He tells them that there was a petition for the man's life; the mender says that the petition is presented to the King himself. But, the men at the fountain whisper that the prisoner will be executed as having committed patricide, and he receives a torturous death as his arm is torn from him and he has lost both legs. Finally, in the morning the prisoner hangs from a gallows over the water, poisoning it. After this story has been told, the Jacques put their heads together: "To be registered as doomed to destruction...the chateau and all the race." The Evremonde family is of interest to Mme. Defarge.
On the following day, the King and Queen pass by on the road, and there is much fanfare played. When the mender of roads is so taken by their jewels and siliks and splendour that he cheers. Wondering if he has failed in the eyes of the Defarges, he asks if he has made a mistake. Defarge tells him that he is the kind they want to deceive the aristocrats so they will suspect nothing when the time comes. Mme. Defarge tells him that if he were to set upon a heap of dolls, he would pick the finest, would he not? And, she asks him if he
"were shown a flock of birds, unable to fly, and were set upon them to strip them of their feather for your own advantage, you would set upon the finest feathers; would you not?"
Today, Mme. Defarge continues the metaphor, he has seen both dolls and birds. Soon, the revolutionaries will "set upon" and "pluck" these dolls and birds, the aristocrats. And, it will be the time of the Jacques to hand their own victims, just as the poor peasant has been hung.
Having gone to see the French aristocracy in all of their glory with other people interested in rebellion, this chapter ends with Madame Defarge creating an analogy between the dolls and the birds that your question refers to and then the lords and ladies that they have just seen, a "glittering multitude of laughing ladies and fine lords" in their full glory, covered in jewels and finery that give testament to their wealth.
Note what Madame Defarge says to the Jacques that is with them:
"If you were shown a great heap of dolls, and were set upon them to pluck them to pieces and despoil them for your own advantage, you would pick out the richest and gayest. Say! Would you not?"
In the same way, we would pick the finest birds to pluck from a dead pile. Having gained the affirmative response of Jacques to these two questions, Madame Defarge that the dolls and birds she refers to have been seen today in the form of the aristocracy. Madame Defarge obviously thus is talking about what will happen when the Revolution begins and all of the aristocracy will be as a pile of dolls ripe for the plucking.