That is a Warnant System Flobert, the last and least weak of the Flobert series of cheap guns. (I won't say "strongest" about any of those little guns.) They sold for $3.00 in the 1897 Sears & Roebuck catalog and were still in the 1911 Alfa catalog. So I would say yours was made sometime between 1890 and WW I. A Remington No 4 true Rolling Block was $5.00 at the time, starting to get into real money and a Winchester Low Wall .22 was $10.13 which was seriously expensive.
Most of these were made in Belgium but I do not see (crown) AS in the chart of Belgian proof marks, and you do not mention the ELG or perron found on most Belgian guns. Not German, either, that I can find.
Grandpa's gun has been reblued and the stock refinished with a lot of buffing and sanding. Maybe the rest of the markings were polished away.