You’ve probably noticed that time is different in The Fall. Jean-Baptiste tells you his life story, but he doesn’t do it chronologically. Either he’s like that guy who can’t tell a joke right, or Camus has done this on purpose. Our money’s on the second interpretation.
Just to be clear, let’s list in chronological order the events that occur in Jean-Baptiste’s confession. 1) Jean-Baptiste occurs the wrath of the motorist and the musketeer watching. Around the same time, a woman jumps off a bridge and he fails to save her. Jean-Baptiste promptly forgets both of these incidents. 2) Years later, Jean-Baptiste hears laughter coming from the water below the same bridge. 3) Only then does he remember the motorist incident and woman he failed to save. 4) These recollections, among many others, constitute a period of "discovery" in which Jean-Baptiste "falls from grace," leaves Paris, and moves to Amsterdam. 5) He ends up sitting at Mexico City with you, acting the part of the judge-penitent.
Now that we’re clear, we can ask why Camus has chosen to disrupt time this way. Why do we hear about the laughter coming from the water before we hear about the woman jumping off the bridge? One explanation is that we get to experience these events the same way Jean-Baptiste did. At the time he heard the laughter, he had already forgotten the woman who died. For him, it felt as odd as it does to us. In other words, we experience a "period of discovery" just like Jean-Baptiste. (Have you seen Memento? It’s sort of the same deal. The movie goes backwards so that we feel the same confusion and uncertainty that the hero does.)
Another possibility is that the disruption of time represents a disruption of cause and effect. This goes back to our much-discussed idea of ‘pulling a Copernicus,’ of "reversing the reasoning" as Jean-Baptiste says. Things are backwards. Nothing makes sense. It’s all very absurd. This makes sense given Camus’s philosophical leanings, and the modernist style in which The Fall is written.