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
Antoine lays out his life and his problems for us: this guy is a complainer. He feels that his daily activities lack purpose, and he is starting to think that beneath all of his concepts and ideas, the world is a totally empty place that is indifferent to all human happiness and suffering.
He tries to overcome this feeling by devoting himself to writing a history book on the Marquis de Rollebon, but the solution doesn't work as well as he'd hoped. His only other relief comes from having sex with a woman he doesn't love and looking forward to the day when his ex lover Anny will visit Paris and meet with him.
Act II
Antoine sits down for lunch with an acquaintance that he calls the Self-Taught Man. They have a brief discussion about their views of the world. The STM claims that he is a humanist and that the only purpose of life is for human beings to love one another. Antoine thinks this is a silly philosophy, since there is no purpose to human life… according to him. The STM, though, will never be convinced that Antoine doesn't truly love his fellow men.
After meeting with the STM, Antoine takes a nauseating walk through the town of Bouville and feels the objects around him closing in. Eventually, his brain totally snaps and he feels like he has finally figured out the truth of all existence. The truth is that the world is made up of things that exist and things that don't exist. Things in his memory don't exist because they're in the past. The only things that exist are in the here and now for Antoine. He doesn't know what he's going to do with this new knowledge. All he knows is that he feels crushed. Womp womp.
Act III
Now that he has (apparently) figured out the truth about existence, Antoine goes to visit his ex lover Anny in her hotel room. He realizes that he was a terrible boyfriend in the past. But Anny says it's too late for him to apologize and get her back. Life has made her into a cynical person, and she no longer believes that life can offer moments of true beauty. She just wants to make herself as comfortable as possible for the rest of her life… which is why she dates older men who spend a lot of money on her. Whoa, jaded.
After their meeting, Antoine watches Anny get on a train and ride out of his life forever. He decides to leave Bouville and visits the library one last time before going. There, he sees the Self-Taught Man get banned from the building for making sexual advances on a high school boy.
When he gets on his train to leave Bouville forever, he thinks about writing a novel. He's had enough of his diary and thinks that he might have better luck giving meaning to his past if he writes a novel. There are no promises that it'll work, but at this point, anything that isn't total despair sounds like a bonus in Antoine's life.