On the morning of his marriage to Lucie Manette, Charles Darnay reveals to his father his true identity.
Charles Darnay is a decendant of the Evremondes, an aristocratic family in France notorious for their oppression of the common man. Before he had been imprisoned, Dr. Manette had had dealings with the Evremondes, and had witnessed their unscrupulousness firsthand. While in prison, the good doctor had written a letter, telling about his experience and denouncing the family, and all their descendants, "to the last of their race" (Book the Third, Chapter 10).
Before Darnay begins his courtship of Lucie, he asks her father for permission to pursue his daughter. He tries to tell Dr. Manette his true identity at that time, and to explain why he had fled France and changed his name, but Dr. Manette is insistent that he not do so until the morning of his wedding to Lucie, if things should so work out (Book the Second, Chapter 10). Things do indeed go well, and on the morning of his marriage to Lucie, Darnay, true to his word, spends a considerable amount of time in conference with Dr. Manette, and when they emerge from their discussion, Dr. Manette is "deadly pale" (Book the Third, Chapter 18). Although it is not directly stated, the reader gets the sense that Dr. Manette has known all along that Charles Darnay is a decendant of the dreaded Evremondes, but to actually hear his suspicions confirmed would be too much for him. Dr. Manette loves Lucie more than life, and for her happiness resolves that
"if there were any fancies, any reasons, any apprehensions, anything whatsoever, new or old, against the man she really loved - the direct responsibility thereof not lying on his head - they should all be obliterated for her sake".
In other words, Dr. Manette knows that Darnay is an Evremonde, but he also knows that Darnay does not share in the family's notoriety, neither in action nor in spirit. For his daughter's sake, he makes the supreme effort to not let Darnay's ancestry stand in the way of their courtship and eventual union. Dr. Manette, whose psyche is extremely fragile as a result of his long imprisonment, only lacks the strength to endure hearing what he knows in his heart about Darnay's identity confirmed, and so to prevent anything from standing in the way of his daughter's potential happiness, puts it off until the wedding day (Book the Second, Chapter 10).