Why did Carton encourage Dr. Manette to continue his efforts to free Charles? What does this say about Carton?

Carton knows Charles is a good man and, more importantly, Lucie loves him. Carton is willing to sacrifice his happiness and even his life to keep Lucie safe and happy.

In the same chapter towards the ending, you will find a conversation between Mr Lorry and Carton, where they talk about "no hope for Charles's release".

As per Carton (as per the conversation), he encourages the Doctor to keep trying for Charles's release, as it might come out consolatory for her (if his plan fails) and she would tend towards thinking that his life was only thrown away or wasted".

This shows the utmost and deepest care Carton has for Lucie. It shows that he really meant it when he made a promise to do anything for her and for the people she loved.

This shows how deeply and truly, Sydney loved Lucie.