I am not sure that this will ad anything of value but here is a partial photo of a Francotte ad from the early 1990's. You will note a certain similarity between this sideplate and the one on Gerry's gun. I don't think that there is a Francotte name on the sideplate.
Here is a closeup of the image.
I can imagine that in the later years that Francotte was in business, it was not making all of the parts for their guns in house but rather buying them from the trade. As has been pointed out, the barrels were likely made by Jean Falla. In fact, in the same advertisement as the above is a one page ad for the Francotte "SuperBritte". This would have been made from one of the (pre-WWII?) SuperBritte barreled actions that were owned by the Britte family. G&H eventually bought those remaining finished guns and barreled actions, SuperBritte's and side by side's, from the Britte family about 2003. A few of the barreled actions have been finished off for G&H by known and respected makers. In fact 20 or 30 years from now someone will probably be questioning the authenticity of one or two Arrieta's that have barrels of Siemen-Martin steel. But I digress.
I think that Francotte was making guns with whatever parts they could obtain and historically consistent markings (other than the proofs marks) were less important than selling an attractive gun from a maker with strong history. And then there are the creative errors of the engraver. The very first G&H Claremont shotguns (by Gamba) had the name "Broadway" engraved in gold on the sides of the action because the Italian engraver was shown a G&H Broadway which was built on the Browning B125 action and told to copy the engraving pattern. So he did, right down to the name.
The Francotte story, especially in recent years, needs to be told. And there are a few employees still around who could do that, but no one is working on it as far as I know.