Your find seems to be a French Army Infantryman's button. Buttons showing ONLY a "flaming bomb" are frequently mis-identified as French Artillery buttons. But actually they were for the "Infanterie De Ligne" -- literal translation is Infantry of the Line, or Line Infantry.
The Infanterie De Ligne buttons shown in the photos below are 1-piece buttons, made from 1871 through 1914. The brass version is from the earlier part of that period. The other is made of aluminum, a metal which was (believe it or not) more valuable than gold until 1886, when an Electrical Refining process was invented. (Sidenote: the "cap" of the Washington Monument is a 100-ounce pyramid of aluminum, chosen because it was a fabulously valuable metal at the time.) Therefore, the aluminum Infanterie De Ligne buttons will only date from the very-late 1800s or the early 20th-Century.
As noted above, the Infanterie De Ligne buttons shown in the photos are 1-piece buttons. Yours is a 2-piece, so it dates from either the 1830s-to-1870, or from after 1914. More research is needed, but for the moment I suspect it is post-1914.
The backmark seems to say "P.Naysville" or "P. Naysvill" (no E on the end) and "Rag___". Please bring it to the Richmond VA civil war relic-show (November 16-17) so I can examine the backmark with a magnifying glass, But if you manage to fully decipher the backmark before then, please let us know.
