Maigret has arrived after a charming old widow, Valentine Besson, travelled from Étretat to the Police Judiciaire headquarters in the Quai des Orfevres in Paris and insisted that she see the Detective Chief Inspector. This is 1950, and a member of the public could get that sort of access in those days. When Maigret is intrigued, he is available.

She tells him that her maid Rose is dead after drinking a sleeping draught laced with arsenic. The sleeping draught was Valentine’s but she noticed it tasted more bitter than usual that night, so she gave it to Rose to take away. Rose drank it herself, although the medicine wasn’t prescribed for her and she didn’t need it.

Étretat would normally be outside Maigret’s jurisdiction, but while he is hearing out the elderly lady in his office, the phone rings and he is called away to the chief of the Police Judiciaire. Charles Besson, Valentine’s stepson and an elected deputy for the Lower Seine region, is apparently unaware that Valentine was going to see Maigret, and Charles has spoken to the minister to ask that Maigret handle the poisoning case.

And so we find Maigret getting up at 5am to take the Le Havre train from Gare Saint-Lazare in Paris, and changing trains at the bleak little station of Bréauté-Beuzeville for Étretat. Here, he looks "at the sea and the white cliffs enclosing the pebble beach; there were boys and girls cavorting in the waves, and others playing tennis at the back of the hotel; mothers sat knitting in deck chairs while elderly couples shuffled across the sand".

Maigret had been born and spent his childhood far inland. He also has a somewhat bitter taste, of memory: "For years, when he was a schoolboy he had seen his friends come back from their holidays, tanned, with lots of stories to tell and their pockets full of shells. He had been earning his living for a long time before he too was able to gaze at the sea.

"He was a little saddened by the realisation that he no longer experienced that little thrill, watching with an indifferent eye the dazzling foam on the waves and the lifeguard with bare, tattooed arms in his boat, which was sometimes obscured from view by a huge wave."

Simenon introduces an air of melancholy into the holiday atmosphere, for today is September 6 and the hotel where Maigret is staying will close on the 15th. "Everything would be closed and the town would look like an empty stage set – the souvenir shops and patisseries would be shuttered, and the deserted beach would be returned to the sea and to the gulls."

Over the years Maigret has carried out several investigations on the coast but, as often happened, the busy detective hadn’t managed to take the time off to go on holiday this summer. Now he is only here because of a criminal case, and without Madame Maigret.

Rose Trochu, from nearby Yport, apparently wasn’t the sort of girl to commit suicide, and hadn’t realised that the medicine would kill her. The poison was intended for Valentine Besson but who would want to kill her? Her husband, Ferdinand, who died five years ago, invented Juva beauty products and made a fortune, but he became over-ambitious and his newer businesses failed. By now most of the money has gone, so Valentine is not rich. Will another attempt be made on her life? No one would stand to gain much from her death, not materially, anyway.

Her other stepson, Théo, is on holiday in the village at the time of the tragedy. Valentine’s daughter Arlette, who is married to a Parisian dentist, was also there on the night Rose died. Arlette slept with another man, Hervé Peyrot, a wealthy wine merchant, in her mother’s house on the night of the poisoning and she has had other affairs too.

The drama is played out against the backdrop of the sea: "As the sun grew redder and the roofs of the houses appeared to be on fire, the sea took on an icy green colour and the world to the east of the setting sun seemed frozen in a surreal eternity."

Arlette doesn’t love her mother. She claims to love her cuckolded husband. Ferdinand once tried to make love to her, his stepdaughter, when she was 18. Théo made love to Arlette once, though she almost forced him into it. Théo also has problems with his step-mother, and didn’t tell her he was in Étretat. The lusty Arlette also makes a move on Maigret but is rejected. It was more an attempt to humiliate Maigret because she felt her actions and admissions had humiliated her first.

At 9pm, "Étretat was a ghost town, and the casino was already in darkness for want of customers. At a street corner there was only one bar with its light on, a café rather, which probably stayed open in the winter for the locals". In the day, the surroundings are "the picture -postcard blue sea, the dazzling white cliffs and the bathers filing down to the beach as if for a photograph".

Maigret, then, must manoeuvre his way through the unfamiliar maze of twisted relationships. "In the beginning he knew nothing, only precise facts, as written in the reports. Then he would find himself talking to people he’d never seen, whom he hadn’t known the day before, and he looked at them as if looking at photographs in an album.

"He had to get to know them as quickly as possible, ask questions, believe or disbelieve their answers, avoid forming an opinion too quickly."

Inspector Castaing is the local policeman who Maigret is assisting. "Two or three times that evening Castaing gave Maigret a sidelong glance, wondering whether he knew where he was going, whether he really was the great detective that young police officers tried to emulate or whether, today at any rate, he wasn’t wasting everyone’s time, or at least allowing himself to be led by events."

Foolish Castaing! Suddenly Maigret has the whole thing worked out. It’s one of those pow, pow, pow Simenon endings, when he appeared to realise that just one more short chapter would tie it all up and he could get back to his favourite cathouse.

Penguin Books is publishing the entire series of 75 Maigret novels one a month in chronological order in new translations from the French. This one, first published as "Maigret et la vieille dame" in 1950, is the 33rd.

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