Various online sources say this was the gare du pont de Flandre, and that was a lift bridge on the canal d'Ourcq about 800 m to the south, which is a bit far to make sense. But having found an 1894 street map, on that it's the Station du Pont de Flandre, which is the bridge over the Canal Saint Denis within 200 m. Such things evolve - urban district names are notoriously fashion-conscious - and even the road that names the bridge was the rue de Flandre, now the avenue de Flandre. Today you might expect la Villette for that location, but the next station to the south was Belleville or Belleville-la-Villette and what's now at la Villette - the Cité de Sciences de Paris - was labelled Abattoirs Généreaux.
When the Métro came (1900) its stops were called stations not gares, which I think follows tramway practice (the Métro being a buried tramway). The urban railway along the PC was presumably thought of in the same way. But the distinction between gare, station, arret, and halte is essentially one of idiom, confusing even to the French, varies between francophone places, and has changed since 1900.
Corentin Cariou metro station was renamed after a local councillor, shot by the Nazis in 1942. Prior to its renaming, it was Pont de Flandre! I suspect that Avenue Corentin Cariou, which leads to the north-west of this station, was originally part of Avenue de Flandre (or Rue de Flandre) which now turns into Avenue Corentin Cariou at or about the point where it passes under the Petite Ceinture. So as you say, it'll be named after the bridge over the Canal de Saint-Denis.
As an aside, the station approach of the old station is, apparently, still called Sentier de la Station
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