For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
The first act lasts from beginning of the novel to the end of Book V. It's mostly stage setting for events that are really going to drive the plot, starting with Quasimodo's trial.
Act II
This section lasts from Book VI to the book's first big climax: Quasimodo rescuing Esmeralda at the end of Book VIII. If you thought things were serious before, they've just been stepped up to a whole new level. You wonder how the heck the characters are going to get out of this one.
Act III
In Book IX, things calm down for a bit while Esmeralda is hanging out in Notre-Dame, but that's just because the action is building up to the big action sequence of the novel: the Tramps attacking Notre-Dame. This final act also contains the novel's final climax: the deaths of Esmeralda, Frollo, and Quasimodo.