Qui n'a plus qu'un moment a vivre
N'a plus rien a dissimuler.
Dust off your opera glasses.
The epigraph means "He who doesn't have another moment to live, does not have anything more to hide" comes from a French opera called Atys, written by Philippe Quinault. It's about a lover who accidentally murders his paramour, so it was probably right up Poe's alley.
But that's not what the quote's all about. In this case, the epigraph reminds us that in all likelihood, this message is probably all too true. It establishes the narrator's credentials because hey, if he's going to die, why would he lie to us?
We also get a hint of the story's action here. After all, if the dude only has another moment to live, whatever's about to go down is certainly not for the faint of heart. The epigraph's like a warning: fasten your seatbelts, readers. Or is it put on your life jackets?