Casual, Condescending, Playful, Confidential
The narrator of "The Purloined Letter" doesn't give us much to work with. In general, he gives the impression of casually telling us a little story with no embellishment and very little of his own personal opinions. Even his first sentence give this impression:
At Paris, just after dark one gusty evening in the autumn of 18—, I was enjoying the twofold luxury of meditation and a meerschaum, in company with my friend C. Auguste Dupin, in his little back library, or book-closet, au troisieme, No. 33, Rue Dunot, Faubourg St. Germain. (1)
This might as well be the lede to a newpaper article: who, what, where, and when. No why, but you kind of get the hint that this is just what the two guys do together.
When G— walks in, we get a little more sense of the narrator's personality, which is a little playful but also has a bit of a condescending edge:
We gave him a hearty welcome; for there was nearly half as much of the entertaining as of the contemptible about the man, and we had not seen him for several years … [he] had a fashion of calling every thing "odd" that was beyond his comprehension, and thus lived amid an absolute legion of "oddities." (2)
Ooh, burn. In other words, G— thinks everything he doesn't understand is odd, and he doesn't understand very much, so he thinks that a lot of things are odd. Clearly, the narrator doesn't have much respect for the guy, and he's got a kind of funny—if mean—way of talking.
Luckily this condescension doesn't seem to be turned on the readers. The fact that the narrator doesn't really comment on what's said in the story suggests that he (1) trusts that both Dupin and G— are telling the truth about things, and/or (2) trusts that that the readers are smart enough to decide for themselves.
Because of this implied trust in the reader's intelligence, the narrator maintains a tone of confidentiality by omitting information that would betray the trust that Dupin and G— have in him. In other words, he can confide in the readers without breaching the confidentiality of Dupin and G—.
This odd mix of snark and honesty makes the narrator a little more interesting than his first, journalistic sentence suggests. He's a guy we wouldn't mind getting to know—although we might be a little afraid of what he'd say behind our backs.