Much characterization exists in "The Prologue" to The Canterbury Tales by Chaucer that reveals the Friar's character, probably the least of which is what he is wearing. The narrator chooses to center on other elements of the Friar's character instead, such as his getting women pregnant then buying a husband for them to keep himself out of trouble (lines 216-128). But the speaker does mention clothes in a few lines:
Not then appearing as your cloistered scholar
With threadbare habit hardly worth a dollar,
But much more like a Doctor or a Pope.
Of double-worsted was the semi-cope [cape]
Upon his shouldners, and the swelling fold
About him, like a bell about its mold
When it is casting, rounded out his dress. (267-273)
The Doctor is actually a scholar with a master's degree, which was extremely prestigious at the time. In short, the Friar wears a great, expensive cape. He did not dress like a poor scholar, but like a wealthy scholar or the pope, who in Chaucer's day was known for his lavish ornamentation. He was wealthy, due to his underhanded and corrupt methods of begging.
Of course, this is indicative of of his character and his vocation. The Friar is all about pleasure and money.
In general, Geoffrey Chaucer does not have very much respect for the members of the clergy who are in his story. The Friar is one of the clergymen for whom he has little respect. This is because the Friar is not really interested in helping people, says Chaucer. Instead, Chaucer says the Friar is interested in living the good life. We can see that in how he dresses.
The main thing we know about his clothes is that the are of high quality. They are not thread bare but are, instead, finely woven. This shows that this Friar is not interested in poverty -- he wants the good life.