This is the second Poirot mystery, first published in 1923. The city where the events take place Merlinville-sur-Mer is imaginary.
The plot, though, starts in Calais where Hastings arrives on a train where he meets Cinderella. Calais is a major port for ferries between France and England.
During the investigation Poirot mentions the Bertillon system. Alphonse Bertillon ( 24 April 1853 – 13 February 1914) was a French police officer and researcher who applied the anthropological technique of anthropometry to law enforcement creating an identification system based on physical measurements. Anthropometry was the first scientific system used by police to identify criminals. Before that time, criminals could only be identified by name or photograph. The method was eventually supplanted by fingerprinting.
The detective leading the investigation of France is Giraud who works for the Paris Surete. Sûreté is a term used in French-speaking countries or regions in the organizational title of a civil police force, especially the detective branch thereof. The Sûreté was founded in 1812 by Eugène François Vidocq, who headed it until 1827. It was the inspiration for Scotland Yard, the FBI, and other departments of criminal investigation throughout the world.
Cherbourg is where Jack Renauld was supposed to set off for South America.
Poirot and Hastings see the Duveen sisters perform at the Palace in Coventry.
When Jack is arrested, the characters mention that if he is condemned, he will go to the guillotine. I have to admit that I didn’t know that the guillotine was still used in the twentieth century. The guillotine continued to be used long after the revolution and remained France’s standard method of judicial execution until the abolition of capital punishment in 1981.