This novel is about Maigret. Oh sure, there’s a murder and an investigation, and we eventually get to know a good deal about the victim and about the suspects, but above all else, we get to know Maigret.
Scotland Yard has heard about the famous Maigret, and with the permission of the Paris police has assigned an inspector Pike to shadow Maigret and observe his methods. Maigret feels terribly self-conscious about that, knowing as he does that he basically has no method, or no method that can be observed in a few days. Pike is absolutely correct in his dealings with Maigret, never imposing himself, always speaking perfect and precise French, and for that reason, and others, Maigret feels oppressed by Pike’s presence, and begins to feel that he must prove himself.
He soon gets the chance: he is called to investigate a murder that has occurred on an island just off the southern French coast. Though it is out of his jurisdiction, he is assigned to the case because the victim had bragged, shortly before being murdered, that Maigret was a good friend of his. Of course, Maigret was not a good friend of his, but had been acquainted with him years earlier, in the course of a criminal investigation.
Maigret and Pike go to the island. It is late spring and the weather is hot. Maigret immediately feels heavy and sleepy and wants nothing other than to simply wander and observe, get the feel of the place. But with Pike watching his every move, he feels compelled to act in a more official way, more energetically. Soon, though, he settles almost into his normal mode: he talks to people, he daydreams, he has a drink. And in the end he catches the killer.
There are something like 70 Maigret novels. If you have never read any, this would be as good as any to start with.