Apart from the two exotic locations, there is another similarity between "Maigret at the Coroner's" (the Tucson book) and "My Friend Maigret" (the Porquerolles one): whereas Maigret had travelled to the United States to study their police methods, and was shown around by Agent Cole of the Federal Bureau of Investigation, now it is Maigret who is doing the showing around, being accompanied by a Scotland Yard detective who has crossed La Manche from London to study French detection methods.

The trouble is, as we dedicated Maigret aficionados know, the Detective Chief Inspector of the Police Judiciaire doesn't actually have a "method", not a conventional one, anyway. Maigret's way of putting criminals behind bars is pretty much his own particular method, and it may not work for other police officers. But, as is said, we should start at the beginning...

Maigret has Pyke hovering in the background but there's been nothing interesting happening since the latter arrived, just routine and paperwork. Uninteresting interrogations. Then Maigret receives a phone call from the police in the south of France to inform him that a man going by the name of Marcellin has been murdered, and what's more he was killed the same night that he had been proclaiming to a bar room of islanders that Maigret was a friend of his.

Maigret can only vaguely recall Marcellin, also known as Marcel Pacaud, and he needs to look in the police records before he remembers him as a small-time crook, a thug, drunkard, thief and pimp – in other words a "mauvais garcon". Their paths had certainly crossed in Paris years ago, but they definitely weren't friends. It was Marcellin's girlfriend, a sex worker, who Maigret helped out of trouble.

The point is that Marcellin was shot dead so soon after his claim of friendship that the police in the south suspect the killer might well have had a grudge against Maigret himself, and was killing the inspector by proxy, as it were. Plus, the police have found an old note from Maigret to Marcellin, concerning the girlfriend, on Marcellin's boat in Porquerolles.

So, it is just the sort of unusual murder case that Maigret himself might like to pop down and look into, by request of the local inspector. And why not get away from the rain of the past four or five days in Paris and take Pyke along to give him something to make his visit more worthwhile?

But there turn out to be two problems for the Detective Chief Inspector. First, the very proper and very British Pyke is a stiff sort of bloke and it's impossible to guess what's going on in his brain. Pyke has been following Maigret everywhere for three days, as discreetly and as efficiently as he can but still it is impossible to ignore his presence. The Frenchman feels like he is under observation. Once, "The Englishman's eye was still fixed on him like the eye of God in the story of Cain".

The two policemen are very different characters, and Maigret feels inhibited and irritated by the Scotland Yard man. Maigret is getting exasperated and it puts him off his stride. He finds he is constantly second-guessing himself and over-analysing everything. He worries about whether Pyke is secretly criticising his drinking, smoking and general behaviour – is he acting as a detective should, and presenting a good example of the French police? He almost seems to be developing an inferiority complex and is feeling very self-conscious. He looks at himself in the mirror and tells himself "That's the divisional chief inspector!" It's as if Maigret is in handcuffs himself.

Second, the laid-back vibe of Porquerolles, just off the French coast, turns Maigret into something of a lotus-eater. As we know, he is often vague when a case is taking shape in his mind, and this wooliness is enhanced on the balmy island where the heat makes him sleepy. It's difficult to find the desire to work. He's in a bad mood and disoriented.

Porquerolles, set in a silky sea that is an incredible blue, is conjured up by the sights, sounds and smells that Simenon scatters throughout the book. There is the aroma of food, of bouillabaise and saffron oil, wine, fresh coffee, mimosa and eucalyptus; and the sound of church bells on Sunday, the noise of the men playing boules, the laughter and conversation in the Grand Hotel and the sound of the sea.

No one has left the island since the murder took place and at first there are no obvious suspects, but gradually Maigret overcomes his lethargy and – as we were sure he would – gets inside the local people, discovers the truth and solves the crime with his usual analysis and intuition. Sooner or later, his fog of ideas usually ends up clearing.

There is the wealthy middle-aged Mrs Wilcox, living on her yacht in exile with her young male "secretary"; the nihilistic Dutch painter De Greef and his teenage girlfriend Anna; a British Major late of the Indian Army; a dentist who threw in his practice, and his family, when he came to the island; a young maid Jojo; and the petty crook Charlot. But why would any of them want to kill Marcellin, who had been living as a beach bum for years?

But, away from Paris, the usual supporting cast is missing – we have to do without Madame Maigret and the so-called "faithful four" Police Judiciaire colleagues Lucas, Janvier, Lapointe and Torrence (who keeps re-appearing despite having been killed in the first official Maigret novel).

This Simenon effort creaks along a bit at times and the main points of interest are not so much the murder and the many suspects but the awkward relationship between Maigret and Pyke, whose "thoughts travelled differently along the meanders of the brain", and the location of Porquerolles, which is actually a real island. Simenon's novel "Le Cercle de Mahe" ("The Mahe Circle"), written three years earlier in 1946, was also set on the island.

At one point in "My Friend Maigret", Maigret "had vaguely promised himself, precisely because of Mr Pyke, to behave as a senior police officer that morning. In principle, a detective chief inspector in the Police Judiciaire doesn't walk the streets and hang out in bars in search of a murderer. He is an important gentleman, who spends most of his time in his office and, from his headquarters, like a general, directs a little army of sergeants, inspectors and technicians.

"Maigret had never been able to resign himself to that. Like a hunting dog, he needed to go ferreting things out in person, scratching and sniffing for scents."

"My Friend Maigret" by Belgian author Georges Simenon (1903-1989) was originally published in French as "Mon Ami Maigret" in 1949. It is the 31st of the 75 Maigret novels, which are being reissued one a month in chronological order with new translations by Penguin Books. It was previously published in English as "The Methods of Maigret".

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