Dr. Manette makes shoes because he made shoes while he was in prison, and when he gets stressed he has a mental relapse and makes shoes.
Dr. Manette was locked in the Bastille prison for 18 years by the Marquis St. Evremonde. His pastime, while he was in there, was to make shoes. He did this to keep from losing his mind.
My mind is a blank, from some time—I cannot even say what time—when I employed myself, in my captivity, in making shoes, to the time when I found myself living in London with my dear daughter here. (Book 2, Ch. 3)
When he got out, he retained his shoemaking tools and went back to shoemaking whenever he was stressed. It is known as regression. One such occasion was when his daughter got married. He found out that his son in law was actually the nephew of the Marquis St. Evremonde, and now that the marquis was dead, had that title. So, the good doctor went back to making shoes because his fragile mind relapsed in order to prevent total collapse.
When Lucy and Charles get married and go on their honeymoon (and Dr. Manette loses it again and goes back to shoemaking), a sort of shoemaking intervention takes place. Jarvis Lorry, who is a close family friend, understands what is going on. He talks to Dr. Manette. Lorry takes the shoemaking materials and gets rid of them so that it can’t happen again.
The burning of the body (previously reduced to pieces convenient for the purpose) was commenced without delay in the kitchen fire; and the tools, shoes, and leather, were buried in the garden. (Book 2, Ch. 20)
Dr. Manette is actually an incredibly strong man. He was “recalled to life” in the beginning of the book, and he overcomes his demons. He was wrongfully imprisoned by the French aristocracy and the marquis to keep him from talking, and he spent many long years in prison. Giving up the shoes and embracing Charles as a son-in-law are all very strong things to do. Unfortunately, the family peril is not at an end.