"Franny" introduces the major themes of the novel, but it's in "Zooey" that the family drama really comes in. The majority of the text is taken up by family arguments: first Zooey and his mother, then Zooey and his sister. Even the narrator is another family member, the absent Buddy Glass. Seymour's presence can of course be felt throughout the story (see Seymour's "Character Analysis" for more). The drama is played out in the conversations between the characters, and the plotline driven by dialogue.
Because of the spiritual nature of Franny's crisis, a good chunk of the text is devoted to religious philosophy. There is a kōan or two (meditative question used in the practice of Zen Buddhism) to be found in Buddy's letter to Zooey (start with the little girl at the supermarket) and again in Zooey's words of advice to his sister (the lady carrying the jug over a hill, the "Fat Lady"). Franny's interest in the Jesus Prayer brings Western philosophy into the mix as well, and the collection of quotations in Buddy and Seymour's bedroom throws in even more philosophical variety.
Because Salinger is so popularly considered one of the great American short story writers, and because Franny and Zooey is interested more in character and theme than in plot or action, we can also classify this work as good old literary fiction.