Colonel March is visited at The Department of Queer Complaints by Martha Pollard, a widow who is dressed, darkly, as though in mourning and in a sense she is, but not for her husband, who died some years ago. She had fallen in love with Pierre, a self-proclaimed artist who she met on the beach in France and they were together for, as she says, “four weeks and three days.” He then left her, taking some of her jewellery with him. Some time later, she sees him again, at Paris airport where he’s flying to England to take part in an Anglo-French fencing competition and she follows him to London – but it’s him she wants back, not the jewels.
It’s at this point that she sees March, though it’s unclear if she has chosen to visit him, or whether the fact that she was carrying a gun has interested March in her. In any case, she says, “If he had refused to come back to me, I might have killed myself.”
March is worried that Mrs Pollard is behaving like “a young girl in the throes of her first love affair” and is concerned by her behaviour. He asks, “Suppose I could prove to you that he’s preyed on other women in much the same manner?” She finds the idea hard to believe, but is not averse to him trying and so March enlists the help of Inspector Ames of Scotland Yard and Monsieur Goron of the French Surêté.
March and Ames visit the fencers at the salle d’armes and await the arrival of Mrs Pollard so that she can identify the man in question. While they wait Hartnett invites March, who used to be a fencing champion, to referee one of the matches – an invitation he gladly accepts. Ames, who has gone out to find Mrs Pollard, returns with the news that she appears to have committed suicide by taking an overdose of sleeping pills. With her was found a collection of press cuttings relating to the fencer René Trenier. Trenier, by profession, is a commercial artist but rather than question him, March and Ames leave.
By following morning, Goron is in England and Ames visits him in his hotel. While Goron consumes his breakfast, Ames explains to him that the autopsy on Mrs Pollard has now been completed and it’s clear that she was murdered, although Ames does not explain the results in detail. He is keen to get Goron actively working on the investigation, but Goron prefers to finish his meal. Goron explains that the result of the autopsy is no surprise: a woman who commits suicide over an affair of the heart will always dress herself in her most attractive negligée, make herself up most beautifully and write a tragic note to the man who jilted her. “That romantic type woman,” he says, “always wants her young man to spend the rest of his life feeling repentant. Which of course he never is.” Goron has also deduced, correctly, that Mrs Pollard was probably suffocated as there were no marks on her body. Ames is deflated.
Ames and Goron interview the fencers one by one and gain little information. Trenier admits that he had met Mrs Pollard once or twice but always when he was with someone else – who he refuses to name. His alibi for the time of the murder is that he spent the evening with Robert Delius. So their last interviewee is Delius himself who confirms that he and Trenier had dinner together, but adds that Trenier left for an appointment at around 7.15. Ames reports to March and tells him that he wanted to arrest Trenier but Goron was against it. March is sanguine: if they get it wrong, Goron will never let them hear the last of it.
Trenier and Delius are talking in the changing room at the salle d’armes, they will be opponents in the deciding bout. Trenier is concerned that the police keep questioning him and pointedly remarks to Delius that he hasn’t told them who Mrs Pollard’s lover was… yet.
March is refereeing and starts the contest. Trenier gets the first score and as they turn away from each other to begin again, Delius secretly removes the safety-tip from his foil. Neither March nor Trenier notice this until the fencing has resumed. March interrupts the combatants and makes Trenier the winner, because of a foul. He arrests Delius for the attempted murder of Trenier and the murder of Mrs Pollard.