It is, of course, the mid third of the 20th century and bra-burning has not caught on in a big way yet, even in egalitarian France. Mme. Maigret wakes Jules each day with his cup of coffee, cheerful. That is, if he is home, because Maigret may still be at the Police Judiciaire carrying out one of those all-night interrogations or he may have been wakened by the phone in the early hours, dragging him out of bed into the cold city and the latest corpse.

When he's on a perplexing case, Maigret becomes gruff and withdrawn but his wife understands his moods. One of her attributes is that she rarely asks him about a case. We much enjoyed this bit of dialogue between them in "Maigret at Picratt's" (1950):

"Are you going out?" (she asks him)

"I'll probably be gone for the better part of the night."

"Has the countess been found?"

"Yes. Strangled."

"Don't catch cold. The radio's saying there's going to be a frost and that it'll probably be icy tomorrow morning."

Mme. Maigret makes the bed, cleans the flat and does the shopping. She looks after her husband as if he were a child, but in a good way. She makes splendid meals for him, not just at dinnertime but also for lunch. Often, he does not arrive to eat them because he is still out solving crimes, but if Maigret misses the foie de veau en papillote at lunch he can still get the chicken with tarragon for dinner.

In fact, their first encounter with each other concerned food. In "Maigret's Memoirs" (1951), the Detective Chief Inspector recalls when he was an apprentice policeman, on a bike. A friend invites him to a party given by some government people and he goes but feels awkward and ill-dressed.

At one point, he is standing next to a full plate of petits fours. He reaches out for one, then, without thinking, another and another. Eventually, he looks down and sees, to his mortification, that he has eaten every last one. Furthermore, other guests have noticed and are staring.

At that moment, a girl in a blue dress comes up to him with another plate of the little cakes. Would he like one? she asks, and advises him that the ones with the candied fruit on top are the best. This is the niece of the hosts, and what she is saying is that Maigret should have all the cake he wants. Her name is Louise but she is almost never called that again, because she is soon Mme. Maigret and this is how she is usually simply referred to.

On Sundays, they often walk, arm in arm, to a cinema. Every year, Mme. Maigret goes to visit her sister in Alsace for a month, and Maigret moves into a hotel because he doesn't like to be at home when she's not there. Physical exchanges between the two are seldom described, despite Simenon's proclivity for mentioning sex. One mild encounter occurs in "Maigret and the Dead Girl" (1954), when the superintendent turns around and kisses her – in bed!

And so to "Madame Maigret's Friend" (1950). She has been going to the dentist for a few weeks and has made it a habit to sit in the little park opposite his surgery before the appointment so as to ready herself for the ordeal. While in the park she has made the acquaintance of a woman (always in a very stylish, lovely white hat and tailored blue suit) who goes there with her little boy.

One day the woman is distressed and asks Madame Maigret to look after her child, saying she'll be back to fetch him soon. Unfortunately, the woman returns hours late, causing Madame Maigret much distress and making her miss her dentist's appointment. When the woman finally reappears, she snatches the child and drives off in a taxi, promising to explain later, which she never does.

Even worse for the domesticity of the Boulevard Richard-Lenoir, the Maigrets' food has been left simmering and it burns and is ruined. Maigret returns to a flat empty of his wife but full of smoke. Still, he has a different problem. An anonymous note has told of a body being burned in a bookbinder's furnace. Only teeth are found in the ashes and there is no report of a missing person and no corpse to work with. The bookbinder, named Steuvels, is taken into custody but nothing can be proved by the police.

By now, we feel we know Simenon so well that we can read him like a, well, book. First mention of a brothel: Page 8. First streetwalker: Page 12. First mistress: Page 31. First breasts: Page 51. Madame Steuvels, the bookbinder's wife, was once – surprise, surprise – a lady of the streets.

In its tight 180 pages Simenon produces his usual quota of strange characters and twists and turns. Where is the missing suitcase? What about the bloodstains on the mysterious suit? For a while the investigation is going nowhere, the newspapers are on the offensive and an angry lawyer is attacking the police in general and Maigret in particular.

Then it happens that the Detective Chief Inspector's wife will play a more significant role than usual. Her encounter with the strange woman in the blue suit and white hat may hold a clue that will solve the mystery.

"Madame Maigret's Friend" is quickly and easily read and a satisfying mystery. Occasionally over the course of the "Maigret" books a loose woman will offer him her delights, but he is never tempted to taste. The faithful Louise is waiting for him in the Boulevard Richard-Lenoir. We readers may have come to love her but not as much as Jules does.

Penguin 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 "L'amie de Mme Maigret" in 1950, is the 34th in the series and was published previously in English as "Madame Maigret's Own Case" and "The Friend of Madame Maigret".

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