Symbolism, Imagery, Allegory
Throughout the book, Frederick is no stranger to fog. He strolls through the thick fog and mist of Paris and Fontainebleau, often while feeling pretty gloomy himself.
In the opening chapter, as the steamer pulls away from the quay and up the Seine, Frederick gazes regretfully back at the city:
Through the haze he surveyed steeples, buildings of which he did not know the names; then, with a parting glance, he took in the Île St. Louis, the Cité, Nôtre Dame; and presently, as Paris disappeared from his view, he heaved a deep sigh. (1.1.4)
Sigh, indeed.
Frederick never completely emerges from this haze, which seems to symbolize his lack of clarity and purpose. He spends the entire novel changing careers and lovers—he even claims to have fallen out of love with Madame Arnoux at a few points. Basically, he's just all up in his head, projecting his emotions onto the city around him.