Jean spent the second half of his childhood in Paris, and Paris is a place Jean longs for. (We could think of it as the geographical equivalent to his mother, or Sister Irma.) New York City is his home at the beginning of 1939, several months after Jean's mother passed away. This New York City is seen through the lens of Jean's grief, and through his growing isolation and loneliness.
The real action of the story takes place in Montreal, Canada, in or just outside a "highly unendowed-looking, three-story building – a tenement building, really – in the Verdun, or least attractive, section of Montreal" (22). The first floor is home of the orthopedic appliance shop outside of which Jean has his epiphanies. The second floor is Les Amis Des Vieux Maitres, the correspondence art school where Jean works for that week and a half in late June/early July. We never learn what's on the third floor.
Since we don't know what the third floor is, and since we take a good look at the orthopedic appliance shop in Jean's "Character Analysis," we'd like to take a good hard look at the second floor. We'd also like to suggest that it functions more as a reflection of Jean's mind at any given moment in the story. It has a fictional feel to it.
The fact that the school is set in a poverty stricken building in a bad neighborhood reflects Jean's desire for a place that makes him feel gritty and starving artisty, and mirrors the poverty of spirit he's feeling in the wake of his death. Ultimately, the building also suggests that one person's poverty is another's art.
Like Jean's mind, the walls of the tiny school "instructor's room" are "hung with many framed pictures […]" (22). This room also has a "no-smoking" rule, which stresses the fact that Jean, a smoker, is outside of his comfort zone. As we discuss in "Symbolism, Imagery, Allegory," the fact that Jean doesn't have any chairs in his room is a big issue. Mme. Yoshoto is more than happy to provide a chair, but he won't admit he needs one. This room without chairs seems to echo Jean's perspective that all kinds of self-denial are in order – that he can't enjoy anything now that his mother is dead. (Still, notice how comfy he becomes when he finally brings a chair up.)
It's also important that Jean hears one or both of the Yoshotos moaning in the night. In addition to lending a nightmare quality to each night, it echoes the grief that Jean is feeling over his mother's death. This approach lets us experience grief ourselves. We don't know what causes the Yoshoto's grief, so can we associate it with all grief in the world. The moaning is also important for Jean. It lets him see that he is not the only one suffering in the world.
When the personality of Jean de Daumier-Smith begins to lose its usefulness, the school built to reflect it crumbles, at least symbolically when it's shut down for lack of license. We can be sure, though, that the orthopedic shop, with all its connotations is still standing.
Be sure to check out what we have to say about the World War II backdrop of "Blue Period" in "What's Up With the Title?"