The setting of the story is Paris in the early 1840's.
Why Paris? I guess it's connected with glorious and most romantic status of this city in contrast with it's dark corners and creepy mysteries. The city produces some Noir effect, although I do not sure, Poe was acquainted with this cultural wave.

        While the dark, smoky room creates a Gothic mood, it also seems decidedly anti-Gothic. People talking, thinking, and smoking pipes in a library seems stable, calm, and not very scary or creepy. (Unless you count Dupin's frighteningly long explanation of how he solved the mystery). There's even something comforting about it. It's a setting perfect for the coldly logical explanation of how Dupin locates and purloins the letter.
Poe just isn't interested here in external details. The story might as well take place in Peoria, Illinois as Paris, France (although Paris does lend a romantic, exotic feel to the story); and if you changed a few of the details, it could just as easily take place in 1945 or 2045. But that doesn't mean setting isn't important.