Comedy, Quest, Satire or Parody
Although the genre of the individual tales varies, the goal of the frame story is pretty clearly to tickle our funny bones and satirize the quirks of various pilgrims, and social estates. So we get lots of humorous details, like that one about the wart on the Miller's nose, or that gross tidbit about the puss-oozing wound on the Cook's leg. As part of the satire, we get characteristics thought to be typical of particular occupations, but exaggerated hugely. Knights are supposed to fight battles? Well this Knight's been at practically every battle ever fought in the past twenty years! Wives are supposed to be lustful (and married)? Well this Wife's had five husbands, in addition to numerous lovers in her youth! So there you go: comedy and satire. Oh, and since this story is about a group of pilgrims on their way to a shrine in a quest for forgiveness, you might also consider this part of the "Quest" genre.