I have not been able to determine if scholars have identified a specific point that mark's the story's midpoint—for Chaucer's The Canterbury Tales. According to eNotes.com, there are twenty five pieces to the tales, which includes a lengthy prologue. The prologue thorough and detailed description of the characters who are traveling on the pilgrimage.
Then, each member of the pilgrimage is supposed to tell a story that has some moral to it. For some, the tale is reflective of the speaker in a good or rational way. (For example, the Wife of Bath is supportive of marriage and may be looking for her sixth husband. Her tale, then, speaks to looking within a woman instead her physical appearance which does not provide an accurate picture of the kind of person a woman is. This supports her argument that while she may not be young and beautiful, beauty is only skin deep, a premise that would serve her well.) In other cases, the tale may ironically point out the short comings of one of pilgrims, even as he shares a story warning the audience of a sin he himself is guilty of. (For instance, the Pardoner's Tale speaks of the vice of greed, and the Pardoner is himself guilty of that vice.)
In terms of the middle of the story, if we were counting, the Friar's Tale is thirteenth, which is about half way through the twenty-five tales. However, in that the prologue is so long, the middle might be located elsewhere. For instance we might be able to argue that the middle is closer to number ten, which is the Monk's Tale. At the same time, some of the tales are shorter or incomplete, so the middle may be somewhere between the tenth tale and the thirteenth, but this is only an educated guess.