NavList:

In answer to Luc's question - how did I track it down?

Frank mentioned in his post that his source was Old Book Illustrations.  Like many here on NavList I have a interest in the history of navigation, celestial and other, and through that a related interst in the history of time and time keeping.  I often search for scans of old books in my areas of interest.  I was already aware of the general impact that railway systems and the expansion of the telegraph had on the need for consistent timekeeping and was also aware that France had not adopted and standard time across the country until late in the 19th century.  The differences in minutes for the various cities on the face of the watch made sense (by eyeball - but without checking relative longitudes).  As they are not (all) ports, my guess was that this might be related to railway travel.

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, but did turn up some interesting reading material including several links to the early 1850s discussing the problem of train times and the different times kept by different cities and actions taken to adopt a consistent method for timetables.  It also turned up the map Luc included in his post.  This gave me a clue as to a possible narrowed search around the 1850s as the "problem" was clearly a matter of some interest around that time.

I have access to academic search tools which link to various databases of records digitized by universities and similar around the world.  I repeated my search there and looked for results for books and publications from from the 1850 - 1870.  The answer came up immediately.  Fortunetly the UPenn scan is open to all.