Dr. Pardon has suggested a vacation in Vichy, where Maigret can take the waters. At 53 he's in good shape, but in need of a break. Maigret and Mrs. Maigret quickly adjust to the Vichy routine, and start to recognize some of the others on their daily walks. Then the news breaks that one of the women they'd often noticed, Hélène Lange, has been strangled, not far from their hotel. Inspector Désiré Lecoeur, of Clermont-Ferrand, who had once been one of Maigret's men, is in charge of the case, but Maigret begins to "consult". Hélène's sister, Francine Lange, arrives for the funeral, and claims she'd hardly ever had contact with her sister, who led a solitary life.
But each month Hélène had deposited 5,000 francs or more in the bank, after returning from various short trips, almost always to different small cities. Lecoeur and Maigret discover, after Francine has abruptly left Vichy when she received a phone call at her hotel, apparently from the killer, that her connection with her sister had been deeper. Finally the man is found, and the story becomes clear. He had been Hélène's lover years before, and she had told him that she'd had his son. Actually, it was Francine's baby, soon after given up for adoption, and drowned in a pond accident before he reached 3. Hélène had been taking money from Louis Pélardeau all those years, leading him to believe it was his son he was supporting, and that he was alive and well.
This report prepared by Dana Samson