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.
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.
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.