Christopher Booker has identified seven forms that plots can take, and we've picked "The Quest" for "The Murders in the Rue Morgue" – why? Because what is a detective story except a quest for the truth of a mysterious set of circumstances?
First, there's the call to action, in which something has gone wrong in the City (in this case, Paris). It's tough to get much worse than a set of murders that leave one woman's body stuffed up the chimney and the other so mutilated that she doesn't look human. But even the grotesqueness of the case isn't enough – it takes the arrest of an innocent man, Le Bon, to convince our hero, Dupin, to get personally involved. It's at that point that he pulls strings with the Prefect of Police to start his Journey of deduction.
Next up, the hero sets out with his companion – in this case, his faithful sidekick, the narrator. Together, they go to the scene of the crime, where Dupin examines everything. He's then kind enough to tell the narrator (and, by extension, the readers) what he's up against in trying to solve this case (this might refer to those "monsters" that Booker informs us the quest journey includes). First, no witness can agree on the nationality of the "shrill" voice they all hear as they run upstairs towards the room from which terrible screams suddenly issue at 3am one night. Second, the killer(s) must have come in and out through the window by climbing a lightning rod and swinging across on a particularly broad shutter – so the killers have to be agile. Third, why was the crime unusually brutal? Fourth, there appears to be no motive. After all, the killer(s) didn't steal the four thousand francs just sitting on the floor of the apartment. Fifth, the killer(s) have to be superhumanly strong to do the kind of damage to the L'Espanayes that was done. So, Dupin's solution has to account for all five of these factors: the weird voice, the agility, the brutality, the lack of motive, and the strength of the murderer. The narrator is baffled, but Dupin has his own ideas: an Ourang-Outang.
You know that expression, always darkest before the dawn? That's basically what this stage of the quest is: the point when our hero seems to be right there – at the peak of Mount Doom holding the One Ring, whatever And then a challenge suddenly arises.
Nothing dramatic happens in "The Murders in the Rue Morgue," but there is this period after Dupin has solved the case when we're stuck waiting for the evidence to come, in the form of this sailor. Dupin spends the time telling the narrator about how he's gotten this far: the rusty nail that proves the killer(s) could've gotten in through the window, the clump of animal hair in Madame L'Espanaye's hand, and the giant finger-shaped bruises on Mademoiselle L'Espanaye's throat, etc. But we're still waiting for proof of how an Ourang-Outang could've gotten from Southeast Asia to central Paris.
The hero usually has to undergo a last test to prove his worth before he gets the prize. This last test is pretty literal in "The Murders in the Rue Morgue": Dupin has set established an elaborate chain of reasoning that seems persuasive to the narrator, at least. But it's not going to get Le Bon off the hook if there's no evidence that anything Dupin's saying is true. So Dupin's deductions have to be put to the test. The person to do that is the sailor who actually saw the murders go down. Dupin manages to draw the sailor out and to get his story, which does support Dupin's points. So Dupin passes his final ordeal.
The goal of any mystery is the solution, so once Dupin gets the sailor to prove his deduction that an escaped Ourang-Outang killed these two women, he's home free. All that's left is the mopping up: Le Bon gets released, the sailor catches and then sells his wayward ape, and Dupin gets to mock the chief of police.