He requested Poirot's assistance for an unknown matter, prior to his murder. It was revealed that he was a fugitive involved in the Beroldy murder 22 years ago, in which he was the killer, but escaped justice when caught, alongside his former accomplice, Jeanne Beroldy.
Paul Renauld was originally Georges Conneau, who was the lover of Jeanne Beroldy and was associated with the murder of her husband under her advice. However, after killing M. Beroldy, he broke up with her and started a new life after escaping from his crime, no longer desired to do her bidding again. Soon, he changed his name into Paul Renauld and got married to a woman named Eloise, before giving birth to a son named Jack.
However, by misfortune, Renauld discovered that his new neighbor was none pther than Mme. Beroldy, now changed into another false identity of Madame Daubreuil. He began to fed up by Mme. Daubreuil's constant torment and blackmail, and started to become worried when his son Jack began dating Mme. Daubreuil's daughter, Marthe Daubreuil. To escape from Mme. Daubreuil, Renauld and Eloise planned to use the same gambit that once killed M. Beroldy.
The opportunity arrived after Renauld had an arguement with a tramp, who died of a fatal and sudden epileptic fit on his ground. Shortly after asking Poirot for help, Renauld disfigured the tramps' corpse to fake his own death. He also staged his own kidnapping and tied up his wife under her own request, before fleeing to the train station.
However, Renauld's plan was overheard by Marthe, who got closer to Jack only trying to gain Renauld's fortune through their marriage, which was a reminiscent to her mother's scheme when she approached Renauld himself. Marthe followed him as he began to dig a grave for the tramp. She stabbed him in the back and pushed him into the hole before burying him.
Renauld's body was discovered on the next day. Eloise originally believed that her husband faked his death successfully, but fainted in sorrow when she saw her husband's corpse in front of her, dead for real.
- The narrative of the story regards Paul Renauld's death as a well-served justice because he's a fugutive, but the fact that he has a genuinely loving relationship with his family, and is liked well enough by his current employees, prevents him from being a completely unsympathetic character.