You meet Jean-Baptiste Clamence in the Mexico City bar, and he begins his "confession." You hear all about his amazing career in Paris, his ease of living, and his self-satisfaction, all lasting right up to the night he heard the laughter coming from the water. When he gets to the part about doubting his entire existence, you’re pretty much committed to the tale, and Act I is over.
This is where things get a little tricky. Act II is supposed to end when we’re as far from the resolution as possible. We’re not sure there is a strict resolution or even a strict conflict in The Fall, so it’s hard to say when Act II ends and Act III begins. Since all of Jean-Baptiste’s fifth and final monologue involves explaining his profession, as well as his relationship to you, it’s a reasonable guess to say that Act II ends with the fourth monologue, a.k.a. Chapter Five.
Jean-Baptiste’s final monologue. All is made clear…sort of.