The proper spelling is "Gerest Berthon".
Martin Gerest was a big name in St-Etienne and in charge at some point of the gunmakers association.
He sold in 1900 to Berthon Bros who sold out in 1922 (or maybe 1910).
The Grand Prize of 1900 was to M. Gerest not to the Berthon.
The Berthons worked at M. Gerest's address.
This is a standard boxlock with light barrels (Drevet was famous for those).
Best regards,
WC-
P.S> look at the next blurb in the link (dated 1900) which describes Courally as being the "Purdey of Belgian gunmakers".