Though I realize the OP asked about characters who might be based on real people, this still seems to fall into the genre of portrayals on TV or in literature. As such, I think this is best suited to Cafe Society. Relocated from IMHO.
The Cliff Hardy books by Peter Corris are also very well known here.
I want to believe that the OP thought “Jessica Fletcher”, at which point his fingers automatically typed “Agatha Christie”.
Piet Van der Valk was the hero detective in a great series of procedurals by Nicholas Freeling, that take place mostly in the Netherlands. An American author, Martin Cruz Smith continues to write a series about the exploits of Arkady Renko that take place in Moscow and other parts of the Soviet Union.
There’s Hercule Poirot, of course, but also Sexton Blake, who’s probably due a bit of a revival.
Russia has Boris Akunin’s wonderful Erast Fandorin novels.
Georges Simenon is one of those Belgian authors that people tend to think of as French; his Commissaire Maigret is French.
You may prefer the Swedish adaptations. I did.
Speaking of Sweden, that country has The Girl with the Dragon Tattoo series.
The Les Norton novels are pretty popular too.
Simenon’s Maigret has already been mentioned for Belgium. He’s still relatively popular although I suspect that most Belgians, like me, are familiar with the character but have never read a single book (there are dozens of them). The TV adaptations may be a bit more well-known as there were reruns until fairly recently.
Derrick was on TV on Friday nights for what seemed like forever. I still remember watching it every week in the late 80s-early 90s and… I don’t know why :D. Derrick was absolutely uncool, the fashions were already very dated by the time I watched the series, there was almost no action and yet it was weirdly fascinating. Kind of hypnotic, actually. When they started running out of episodes, they turned to other German series but none of them caught my attention as I found them all boring. Well, Derrick was kind of boring, too but… unique.
As Krav Marga etal mentioned, Cliff Hardy [Peter Corris] and Les Norton [Bob Barrett] both adding to their Australian detective franchises from time to time, but none of their recent offerings has set my world alight.
Peter Temple’s Jack Irish novels, and the TV adaptations starring Guy Pearce probably make him the default best-known contemporary PI. Quality of both books and adaptations is pretty good, although not nearly as good as his other Melbourne cop series, which includes Fatal Shore.
In ancient Greece, Sophocles’ Oedipus Rex could be the oldest detective story, with Oedipus as detective trying to locate a murderer who turns out to be himself.
Dirk Gently.
You forgot Batman.
Lord Peter Wimsey.
If you have a Catholic Bible, there are two mystery stories from the Apocrypha. Both Susannah and ***Bel and the Dragon ***are mystery stories. Susannah is a sort of Perry Mason mystery in which the prophet Daniel breaks down lying witnesses under cross-examination. And ***Bel and the Dragon *** had Daniel trying to figure out what really happens to the sacrifices being offered to the dragon idol.
Would Sophocles still be older? From when does the Apocrypha date?