This isn't the place to have essays written for you...but here's some information to get you started:
Conflict, it can be said, drives a story. It keeps it moving forward, provides motivation for characters to make choices, and makes for interesting reading. External conflict may be experienced as a man vs man, man vs nature or man vs society, while internal conflict is man's conflict with himself or internalized ideas of right and wrong. Tale of Two Cities has both types.
An obvious external conflict in the novel is the French revolution...man vs society.
Darnay's conflict is man vs society because he is arrested for being a part of the nobility.
Man vs self: Dr. Manette's struggle to remain sane while he was in jail and to remain sane once he is released. We see this in the fact that he takes up shoemaking to distract his mind from the horrible memories.
Sydney Carton also deals with man vs self in that he is self destructive and jealous of Darnay. In the end, he resolves this by making the ultimate sacrifice.
