NavList:

Murray Buckman,

Like Luc, I wondered how you found it. The story of your search for this watch face is impressive. As I was reading, I kept expecting to run into the line, "and the rest was easy" or something like that. Instead it was a cliffhanger at every phrase. You wrote:
  "So I searched Google, Google Books and Archive.org using various French terms but in general combinations of "chemin de fer" & "horloges de Paris" & montre, together with various of the cities named on the watch. Those searches did not turn up the answer..."

Like that!! Ha! I was on the edge of my seat. :)

Your general approach was similar to mine (though I found nothing). I immediately thought railroads and mid-19th century. Early in the century, railroads were too primitive and not much bound by schedule. By the end of the century, "zone time" was rapidly taking over from local mean time in western Europe as well as in the USA. There were only a few decades when a watch like this would have made sense. I counted the watch as relevant for NavList since those offsets by times to various cities in towns in and near France just scream out "time is longitude!" The Earth turns one degree of longitude in every four minutes of time, and there it is on the face of a watch in plain sight. 

Again, impressive search work, and thank you for finding it. 

Frank Reed