I would say that the climax of this book is the point when Defarge reads the letter during his trial. The letter is one that Manette wrote. It shows that Darnay is related to Evremond, an aristocrat who was guilty of various crimes.
Once this has happened, the book moves into its falling action. In the falling action, we are going to find out what happens to Darnay once this information is revealed. We will find out what is going to happen with respect to his death sentence -- will he die? If not, how will he be saved?
There are two, if not more, climaxes in this novel.
1. Sydney's determination to sacrifice himself for Lucie's happiness
2. Madame Defarge's accidental death from her own gun.