Ha, Ha, ha...Got news for you, Robert-the first two guns and the "Darne" guns listed in your post are not "Darnes" at all-they are Francisque Darne guns. One has to be careful not to get the two distinct manufacturers confused.

Darne Fils roughly translates to "Darnes son", or, "Darne junior". You can get better descriptions of the guns in the Jallas & Cie era (1936) Francisque Darne catalog, available as a reprint from info arms.
Best,
Ted