Is that a Lombardic "H"? Some King Henry (Henri)? (Or is it an "R"? Looks much more like an "R", in which case that scribbly "Henry-something" attribution on the old 2×2 flies out the window.) As of this typing the coin is in my safe deposit box at work so I can't provide weight and diameter just yet. Vaguely speaking, it's in that middling range between the diameters of a US nickel and quarter, perhaps closer to the latter. In hand it kind of feels like a Spanish 2-reales of this era, if you know what I mean. It is obviously silver. Any ideas?
A "K" for Carolus/Charles? Wow. I didnt see that coming. Wouldn't have even been sure they had "K" in their alphabet then. After all, the Spanish don't use it, except for foreign words, so I wouldn't necessarily have expected to see a K on a 400-500-year-old French coin. Edit - now that I remember it, though, there were K's on some of the coins Henry VIII of England struck during his marriage with Catherine/Katharine of Aragon, so ... Thanks!
So much for assumptions. Apparently these douzain/dizain coins were struck in billon. So debased silver, anyway. Thanks for steering me on the right track, @Mark Metzger. The misattribution on the 40-50-year-old 2x2 had thrown me for a loop.