In France the police in the countryside was the Gendarmerie impériale, which was under the control of the army. Here is their uniform.

I saw the history of a single French village. I know that there has never been a police force in it, but there was a mayor. If a very bad problem happened, people would have gotten to the mayor. And he would have sent for gendarmes in the larger village nearby.

Edit: I was wrong when I said Gendarmerie nationale, it was the Second French Empire at the time.