Here are some old plates illustrating the model Dr. Summerfield identified. You can see that the lines of the barrel are identical to mine with the exception of the breechface, which in the old drawings features a typical knob-type cascabel. Mine is a different shape in that area, which I believe is the remains of a tiller for aiming, or "monkey tail."

Now it is apparent to me that there were two sub-models of this basic design, one for land use as shown in the drawings, and another apparently for naval use, which is the type I have. The theory that mine was intended for naval use is strengthened by the fact that it shows the typical features of the well-documented line throwing conversion that was applied to other models of French naval swivel guns.

Two of the drawings of the French M1757 one-pounder "Rostaing" gun:
http://i17.photobucket.com/albums/b62/cannonmn/miscforumsetc/forums4/Rostaing1.jpg
http://i17.photobucket.com/albums/b62/cannonmn/miscforumsetc/forums4/Rostaing2.jpg

The photos he sent of the small bronze French gun at St. Petersburg do not match either my gun or the drawings I've posted here. The size of the St. Petersburg (Museum of Engineers and Artillery) example is similar to mine, but the profile and mouldings do not match.