I have never heard this name before, so I checked several reference books. The name was reported by an old time Ohio Collector, Forrest Tilton, years ago as a gunsmith in Stark County, Ohio, 1850-1860. However, none of the later Ohio books by Hutslar or Whisker mention the name, suggesting they had never seen such a barrel mark, or had not been able to find a documented source for the name.
Your rifle appears to be an original old gun... but it also appears to have been heavily modified from its original condition. The patchbox is an earlier Lancaster, PA style, but when your photo of the box is enlarged, it gives the impression of being a much newer box added to an old, original rifle. The engraving quality is much inferior to an original Lancaster box, and looks modern to me, supported by almost no patina/oxidation on the box. It is more difficult to assess the carving, but it has an amateurish look to me, incorrectly shaped at wrist, etc., and while possibly original, I tend to think it is also a much later added detail, probably when the gun was "restored" in an effort to increase the value of a somewhat plain old rifle.
As to the "Francios Gome" name on the barrel, it does seem to have some patina similar to the barrel surface. But IF, and I really mean IF, such a gunmaker existed in Ohio in the 1850-1860 period, the gun's style, stock shape, etc., is wrong for a rifle from that area and period... and the patchbox is wrong for that time period and area. I cannot explain why the stamped letters have a good, darkened appearance, but they appear to be individually stamped with machinist stamps, which I do not believe were used by any original gunsmith back in the mid-nineteenth century and is much more likely a modern effort to make the gun look like it was made by an old-time gunsmith. If it were an actual gunsmith's stamp from back in that era, it would have more uniform lettering all on the same line from a one-piece stamp.
I apologize for being somewhat blunt on this rifle, and I hope you continue to use this site as you grow into this fascinating hobby of collecting early American longrifles, but I think you might have picked up a heavily "reworked" old rifle this time with non-original, added enhancements to increases its value, which damages rather than helps its collector value.
Shelby Gallien