Erik,
I would agree with Raimey and add this. As early as 1896, Von Lengerke & Detmold were advertising that both the Pigeon weight and the Featherweight Francottes "although doing good work with black powders, are bored and intended for Schultz and E.C. powders specially". Schultz and E.C. were early Nitro powders. Now of course Justus Von Lengerke had interests in several smokeless powder companies and apparently spent considerable time and effort promoting its use on the live pigeon circuit, but not without justification. The marketing hype of a long-gone retailer does NOT offer a justification for shooting a 100 year old firearm with modern ammunition but it does suggest that the Francottes were not black powder proofed only.
As concerns the Blue Book, the Francotte section is worse than useless. There are no descriptions of any of the models of Francotte shotguns made before 1910 and that were sold by VL&D and VL&A, probably including yours. And the descriptions of the models made after 1910 are incomplete and inaccurate. Even the Francottes offered for sale by dealers today are frequently wrong as to the model, and prices can be all over the place.
If you will post the serial number of your Francotte I'll see if it might be in the VL&D or VL&A records and, if so, I'll tell you the model. If the number pre-dates 1901 (when our VL&D records begin), we may be able to identify the model from photos and a description of the features of the gun. Knowing the model won't make it any more shootable but at least you will know the relative value when it was made.