In A Tale of Two Cities, why does the Farmer die in Chapter 1?
The style and writing of Dickens is actually very complex and difficult to understand at first reading, and the first chapter of this great novel is no exception. The passage you are refering to in Chapter One does not actually include a literal farmer as a character. Rather, Dickens is personifying death as a farmer just as he personifies Fate as a woodman to foreshadow the violence and death that will occur in France in the subsequent years. Let us note what he says precisely:
It is likely enough that in the rough outhouses of some tillers of the heavy lands adjacent to Paris, there were sheltered from the eweather that very day, rude carts, bespattered with rustic mire, snuffed about by pigs, and roosted in by poultry, which the Farmer, Death, had already set apart to be his tumbrils of the Revolution. But that Woodman and that Farmer, though they work unceasingly, work silently, and no one heard them as they went about with muffled tread: the rather, forasmuch as to entertain any suspicion that they were awake, was to be atheistical and traitorous.
Hopefully, reading this passage once again will help you to see that the Farmer and the Woodman, as indicated by their capitalisation, are not literal characters but are rather personifications of death and fate respectively. Therefore Dickens is not saying that a farmer died, rather he is using this stylistic technique to comment upon the way that the groundwork for the French Revolution is already occurring, albeit imperceptibly.