We have turned up some new research on the clock. Our contact in France (that goes by the handle laprade) was able to contact the president of the association The Friends of Old Issoudun. Apparently, the president has a Comptoise clock with the Fremion name as well. They found old postcards at least as old as 1910 where you can see the market square, including a watchmaker "Fremion." It could still be seen there as late as 1930.
In 1927 there were 7 watchmakers and jewelers in Issoudun. By 1936, Fremion was gone, but there was still a jeweler/clock shop there under a different name until 1960, when the whole block was destroyed.
I couldn't find the actual postcards online that they talk about. These above are some random old postcards from Issoudun that I found here. If there are any postcard collectors out there, I'd love to hear if you can find these cards!