Randy,
Unfortunately there is no Francotte book, and of course, the company itself is now out of business. G&H can be of great help with some of the guns, but the earliest guns fall outside their records from what has been posted. Early VL&D catalogs are your best bet for determining the model specifics of your gun. Unfortunately the only Francotte catalog repro readily available is not especially relevant to your gun. I have a portion of an 1892 catalog but it is focussed on other models - sorry not to be of more help.
The A&D patent use number in the breech face and the "Not for ball" mark on the barrel flats should narrow the production window pretty tightly. I am away from my proof mark books so I cannot check the exact dates on the "not for ball" specifics, late 1880s to 1890s from memory, but another poster will have the exact date I am sure. The specific A&D patent use number would indicate a gun made sometime in the very late 1880s timeframe.
Looks like a nice gun - congratulation on the acquisition.
Ken