Never before had he seen more lustrous dark skin, a more seductive figure, or more delicately shaped fingers than those through which the sunlight gleamed. (1.1.23)
The first time Frederick lays eyes on Madame Arnoux, he sees that she's smokin' hot. Every part of her body calls out to him, and our narrator doesn't hesitate to recount it all for us. Does anyone else feel a little voyeuristic? Does Frederick?
He longed to become familiar with the furniture of her apartment, all the dresses that she had worn, the people whom she visited; and the desire of physical possession yielded to a deeper yearning, a painful curiosity that knew no bounds.
Frederick's obsession with Madame is almost immediate, and this "painful curiosity" is just the beginning. But wait a second—how on earth are we supposed to reconcile this "desire of physical possession" with the fact that the two are never sexually involved?
Whenever a woman was walking in front of him, or coming in his direction, he would say: "Here she is!" Every time it was only a fresh disappointment. The idea of Madame Arnoux strengthened these desires.
Okay, it's that bad. Everywhere Frederick looks, he sees her, as if he's in a bad (read: we watch it all the time) romantic comedy. This woman—or rather, this woman's sexy look—becomes Frederick's primary motivation for his every move.
Where, then, did she reside? How was he to meet her now? Once more around the object of his desire a solitude opened more immense than ever!
Is his sexual desire for this lady become emotional at this point? Or does he still just want to track her down for her body? Also, why doesn't he just Google her? Geez.
One thing caused astonishment to himself, that he felt in no way jealous of Arnoux; and he could not picture her in his imagination undressed, so natural did her modesty appear, and so far did her sex recede into a mysterious background. (1.5.184)
Madame Arnoux is so modest that Frederick finds it hard to even imagine her naked. And of course, even when he finally gets a chance to, he turns it down. What the what?
Ere long the conversations were interrupted by long spells of silence. Sometimes a species of sexual shame made them blush in each other's presence. All the precautions they took to hide their love only unveiled it; the stronger it grew, the more constrained they became in manner. The effect of this dissimulation was to intensify their sensibility. (1.5.27)
In their intense emotional affair, Frederick and Madame Arnoux keep it strictly nonphysical. That doesn't mean that they don't have the desire—they apparently just have heaps of self-control.
"It must be nice to glide in the water and feel oneself stroked all over." (1.4.117)
Louise has a passion for Frederick that's awkwardly but violently physical; here, she envies the way fishes live. Hey, to each her own.
But the clerk had theories of his own. All that was necessary in order to get a thing was to desire it strongly. (1.5.252)
Deslauriers functions under the philosophy that if you want something badly enough, you'll get it. That sort of holds true with Frederick, so why does he blow it?
Having seen nothing of the world save through the fever of his desires, he pictured it to himself as an artificial creation discharging its functions by virtue of mathematical laws. (1.5.296)
Deslauriers has his own desires. But unlike Frederick, he's able to control his desires through his impulse to be reasonable. Not as interesting as Frederick, sure, but certainly (slightly) less tortured.
He tramped about till evening, rolling the yellow leaves under his feet, inhaling the fog, and jumping over the ditches. As his arteries began to throb more vigorously, he felt himself carried away by a desire to do something wild. (1.6.14)
Unable to win the love of Madame Arnoux, Frederick begins to fantasize about other possibilities. But it's too late: he's already trapped by his desire for her.
He was seized with a stronger desire than ever—a frantic, ravening lust. Yet he also felt something he could not express—repugnance, a sense of horror, as of an act of incest. Another fear restrained him—the fear of the disgust that might follow. Besides, what a nuisance it would be! And, partly from prudence, partly to avoid tainting his ideal, he turned on his heel and began to roll a cigarette. (2.19.26)
Just as he's about to get Madame Arnoux where he wants her, Frederick chickens out. Why? He's afraid she won't live up to the ideal he has created over the past 20 years.