Monsieur G— is the prefect, or head, of the Paris police. Like Dupin and the narrator, he's in all the three of the Dupin tales of detection. And, like both of them, he's a pretty familiar figure: the doofus policeman who can't match either the detective or criminal.
But he's also the winner of the game of the purloined letter, assuming that "winning" means taking the letter—like winning at the game of marbles. At the end of the story, he's the one running off with the envelope to collect the big reward.
Now, we don't know if G— manages to get the letter back to the royal lady and collect the enormous reward, or if D— (or someone else) purloins it from him before he has a chance. If he gives the letter back to the lady, and claims the reward, then he's really won the game in the sense that he's managed to put the letter back in its rightful position. So, maybe he's smarter than Dupin and the narrator say he is, after all—he doesn't let his cleverness outwit his sense. (Check out "What's Up With the Epigraph?" for more on "cleverness" and "sense.")
G— is the prefect, and that's pretty much all we know about him. His top priority is getting the letter back: (1) for his "honour" (36); (2) the "enormous" prize (36); and (3) something like chivalry, since he doesn't want D— to have the royal lady under his thumb.
We also know that he's diligent in his search. He tells Dupin and the narrator that:
For three months a night has not passed, during the greater part of which I have not been engaged, personally, in ransacking the D— Hotel. (36)
And then he really steps it up by bringing in Dupin and conducting another exhaustive search of D—'s hotel room. So, he obviously takes his work very seriously.
But check out the kind of work he's doing. Sure, the letter was stolen, and recovering stolen property seems like a proper job for the police, right? But recovering of the letter actually means re-covering (see what we did there?) a secret. He's aiding and abetting the deception being practiced against the king—and by extension the entire country. After all, the queen has let herself get put in a position where D— can apparently manipulate the court's entire political situation. Not too cool.
Since the matter is strictly confidential, the reward is starting to sound a lot like a bribe. It's not as if the royal lady could publicly advertise that her letter had been purloined. Unless G— is loyal to the royal lady for reasons beyond money, he's kind of extorting her, too. She needs him, and the only way she can guarantee his cooperation is money.
Notice also that an ordinary citizen couldn't call in the police for this kind of work, though, we assume, a citizen with enough money certainly could. So, G— is meant to seem rather crooked and corrupt. This is probably part of why the narrator says he's "contemptible" (2). Just in this one situation G— ransacks not only D—'s place but the neighboring houses as well. He also has keys that "can open any chamber or cabinet in Paris" (36). It sounds like G— might abuse his power, both in service of the queen and otherwise. He's a corrupt player in a corrupt system.
If this is a game that G— won, there must be something to his method that Dupin doesn't see. We know that he's diligent and thorough:
Why, the fact is, we took our time, and we searched everywhere. I have had long experience in these affairs. I took the entire building, room by room; devoting the nights of a whole week to each. We examined, first, the furniture of each apartment. We opened every possible drawer; and I presume you know that, to a properly trained police-agent, such a thing as a secret drawer is impossible. Any man is a dolt who permits a "secret" drawer to escape him in a search of this kind. The thing is so plain. There is a certain amount of bulk—of space—to be accounted for in every cabinet. Then we have accurate rules. The fiftieth part of a line could not escape us. After the cabinets we took the chairs. The cushions we probed with the fine long needles you have seen me employ. From the tables we removed the tops. (47)
He's thorough, all right—but he's also ordinary. This is all breadth and no depth (or is it all depth and no breadth?). In fact, he's so thorough that he even knows to consult outside help when his own methods aren't working. Asking Dupin for help just might be the cleverest thing that he does.
And notice that Dupin's success is only possible thanks to the ninety days of work G— does before he visits Dupin. Dupin even admits that he only figured out that the letter was probably out in the open after hearing "decisive evidence" (110) stating everywhere that the letter was not.
The point is: both methods were necessary to solve the crime. Dupin and G— need each other, and G— admits it.
As the head of the Paris police department, the royal lady's confidante, and the guy with the keys that "can open any chamber or cabinet in Paris" (36), G— knows an awful lot. There's something ultimately creepy about a person who creeps around in the dark looking at other people's stuff, and you have to admit that the story sounds an awful lot like gossip.
Come to think of it, we never do find out exactly where G— gets his information. Presumably, everything he tells Dupin comes from the royal lady—but we don't know for sure. We also don't know what he's going to do with the letter. Sure, he'll probably give it back, since he seems pretty eager for the reward and praise. But is he going to read it first?
And, for that matter, why doesn't he seem curious about where Dupin found the letter? You'd think that, after spending four months searching for it, he'd be at least a little curious. Instead, all he wants to do is collect his reward. This is a guy who doesn't actually seem to care too much about knowledge. He doesn't want to learn from Dupin; he just wants to get results.
"Ha! ha! ha!—ha! ha! ha!—ho! ho! ho!" roared our visitor, profoundly amused, "Oh, Dupin, you will be the death of me yet!" (15)
If this were your ordinary Poe tale, we'd know right away that G— wasn't going to make it to the end of the story. Here it seems more like a tease, or something meant to set the Gothic mood of the tale.
But you know what? Considering that this seems to be only one episode in the long history of the purloined letter, and since Dupin went out of his way to rub the theft in D—'s face and seemed to fear that D— might kill him if he caught him in the act…maybe we are right to be a little worried about G—.