If we look at Book II Chapter Nine of this great novel, we can see the confrontation that Charles and his Uncle have. Even though Charles has returned to France at his Uncle's bidding, it is clear that he in many ways wished he had not returned. Although he is polite towards his uncle and never insults him or angers him, the way in which he finds everything his uncle stands for distasteful and horrid. Therefore, although Darnay does feel some link to his uncle because of the blood that they share, at the same time I would hotly debate that he actually "loves" him. Note the way that Darnay talks about how he despises being part of the aristocracy:
"And has left me," answered the nephew, "bound to a system that is frightful to me, responsible for it, but powerless in it; seeking to execute the last request of my dear mother's lips, and obey the last look of my dear mother's eyes, which implored me to have mercy and to redress; and tortured by seeking assistance and power in vain."
Again and again in this chapter, during their conversation together, Charles gives ample evidence of the way in which he hates the corruption and arrogance of his family and the way that because of it so many peasants have suffered and continue to suffer.
Darnay does not really love his uncle. He said he would even denounce the family name and property once his uncle dies.
In book 3, chapter 10, Darnay as a young child promises his mother that he will be faithful in doing what is right. His mother's influence, which is more against the family name, leads him to "hatred" (I don't think he hates his name, but would rather not associate with it) of his name. Darnay doesn't even go by his family name, and seeing that in the beginning of book 3, it gets him into trouble.