That‘s in fact something that frequently trips up Germans speaking English. German does have a simple past called Präteritum: ich kaufte=„I bought“ but it has been displaced in oral usage beginning with the 13 century in the Upper German regions (oberdeutscher Präteritumschwund) und arriving in the north by the 20th century, by the Perfekt: ich habe gekauft=‚I have bought‘. To use the Präteritum in conversation nowadays sounds pretty stilted. Which is why we Germans are apt to say things like ‚my milk teeth have fallen out fifty years ago’ in English.
By the way, (in English) “have” is not the only verb that can have an auxiliary or light or modal predicate content:
The sun will rise tomorrow.
I am going to watch television.
She took a shower.
And the omnipresent « got ». Two of my francophone roommates asked me to try to explain it. It’s impossible.
It’s not so much that Maigret is pulp fiction, but the slightly startling (to me) fact that when Maigret interrogates the perp at the end of the tale, the latter tells his story in the passé simple.
My wife tells me that when she took a history course during a year in France, the prof related the historical events in that tense.