Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Omniscient)
The narrator of the "Clerk's Tale" has a fairly unlimited perspective on what's going on in the characters' heads... when he chooses to use it.
And he doesn't always choose to use it: although we learn about the internal workings of Walter's mind—and even, at one point, of Janicula's—he remains completely silent when it comes to the secrets of Grisilde's heart. This silence is probably intentional, meant to set Grisilde apart by making her seem more enigmatic—or perhaps, like she's on a higher, unapproachable plane.
Still, we know that the narrator is omniscient because he tells us, for example, that Walter "in his herte longeth so / to tempte his wyf," or that Grisilde's father Janicula "was evere in suspect of hir mariage" (451-452, 905). At one point, the narrator even predicts the future, remarking that "God be thanked, al fil for the beste" (718) in reference to the outcome of Grisilde's trials. So that means that if he wanted to tell us what Grisilde is thinking, he could. He just chooses not to.
Now, although the narrator is primarily third-person omniscient, he occasionally lapses into a first-person perspective in order to comment upon the story as he's telling it. "I blame hym thus," he says of Walter, "that he considereth noght / In tyme comynge what hym myghte bityde" (78-79). Later he very emotionally condemns both Walter's tormenting of Grisilde and the townspeople's lack of loyalty to her. Thus, what we really have in the "Clerk's Tale" is an omniscient third-person narrator, but not an uninvolved one; the teller of this tale is very much emotionally invested in his story.