At first it appears that the millionaire's son is the culprit, given that his father didn't approve of his choice of a fiancee and he wrote him out of his weeks just two weeks before the murder. However, Poirot digs deeper and finds out that the millionaire is not Mr. Renaud but really Mr. Conneau who had fallen in love with Mme Beroldy. He murdered her husband but then found out she wanted to marry someone other than him. He fled to Canada.
In Canada he gains a wife and a son. He makes his fortune in South America. When he returns to France, he is unhappy to discover that his neighbour is Mme Beroldy. To make matters worse, Mr Conneau's son and Mme Beroldy's daughter fall in love. Mme Beroldy starts blackmailing Mr. Conneau regarding his crime of 22 years before. He devises a scheme to fake his own death. He finds the body of a tramp and digs a grave. However, before he has a chance to bury the body, someone murders him and puts his body in the grave. It turns out that Mme Beroldy's daughter overheard Mr. Conneau discussing his ruse and murdered him.