I think Darnay should not have told Lucie who he was or that he was going to France. Darnay selfishly put them in danger by going to France, and taking them with him was the height of foolishness. In doing so, he set in motion a chain of events that was irrevocable. Darnay could have accomplished what he needed to without going to France though. There were other ways he could have rescued Gabelle.
Secrets are generally not a good idea, of course, as they tend to come back to haunt us. Here, the secret of Charles's aristocratic birth had been entrusted to Lucie's father, so it was known, just not to her. The fact that he had to leave without telling her any details is excusable to this extent: He didn't want to worry her; he didn't really think he's be in any personal danger; he hadn't told her of his past, and to do so in a letter now would be fairly shocking; he was shaken by the idea that his lack of foresight and provision had caused a faithful servant and friend to be imprisoned. Given those factors, he was doing well to leave much in the way of a letter at all. I know he left letters with Manette and Lorry to dispose of his affairs if necessary, but I'm not convinced he really knew what was ahead of him or he'd have re-thought how he took this journey.
Darnay sees his former life as something that he is completely dislocated from, until he receives the pitiful note from Gabelle asking for help. Remember he has renounced his inheritance and any share of the Everemonde family riches, heritage and wealth, which he sees as essentially corrupted by their actions. He has also established a new identity for himself in London as a teacher of French literature. It is part of his desire to protect Lucie that leads him to keep his past secret from her, as well as the request of Dr. Manette when he reveals his identity to him before he and Lucie marry. To tell Lucie would taint her with the same questionable past that Darnay still suffers from.
Before Darnay marries Lucie, he agrees to her father's request to not reveal his true identity to Dr. Manette's daughter as she would reject Darnay out of loyalty to him. (Later in the novel, the reader discovers that Darnay's father and his uncle are the young men involved in the incident that led to Manette's imprisonment.)
Now, in Chapter 24 when Darnay, the Marquis de Evermonde, receives the pleas of Gabelle who has been arrested for following his master's instructions, his honor will not permit him not to return. Darnay ponders the honor of old Mr. Lorry who risks harm in order to serve Tellson's Bank; he thinks that he may be able to "stay bloodshed, and assert the claims of mercy and humanity." Moreover, he feels the magnetic pull of Fate as he senses the "influence of the Loadstone Rock."
A "hard matter to preserve the innocent deceit" to Lucy, he does write a letter telling her of his journey, but not the real purpose. As a man of honor, Charles Darnay keeps his promise to Dr. Manette while obeying "noblesse oblige." For, he cannot be the noble character that he is unless he acts in such a manner.
Without Darnay's being such a noble character, the actions of Sydney Carton to save Darnay at the novel's end can have no nobility nor credibility. Afterall, Carton's famous line has much significance because of Darnay's honorable character:
It is a far, far better thing that I do, than I have ever done; it is a far, far, better rest that I go to, than I have ever known.
Yes, he should of, just in case something bad happened and Lucie got taken hostage, etc.