, I think it's very possible that it was made to carry a 12-pounder.
There are many clues in the photos that make it unnecessary to resort to pure guessing. One is the tube's weight in French pounds, as I mentioned previously. As far as the carriage is concerned, look at the 15th photo in the gallery linked above, same one as that showing the tube's weight. Here's a little logic chain that I think helps size up the carriage, even if I'm not using precise numbers.
I "measured" the diameter of the trunnion on the image on my 'puter screen, with a dial caliper. Admittedly this is useless unless compared to another measurement taken from the same image in the same direction, so I did that to compare. Image trunnion dia: 56mm. Image trunnion rest dia: 62mm. Simple Math: 62/56=1.07 (107% if you like % better)
Why bother with that? We know (goin' from memory here) a French 4 pounder would have a bore diameter of about 3.4 inches. Traditionally, trunnions on "guns" are made with same diameter as bore, so assume trunnion is 3.4 in. diameter. 3.4 in. x 1.07 ratio = roughly 3.8 in. diameter for the trunnion rest of the carriage.
Assume again that trunnion dia. = bore dia., so we're looking for what size of French cannon had approx. a 3.8 inch bore diameter. I think that would be a 6-pounder, but in any case a whole lot less than the bore dia. of a French 12-pounder. We don't know the period of that carriage but it looks 19th C. to me, and for all we know could have been for a rifled gun ca. 1860 rather than a smoothbore, so there the comparisons get more complex.
Does that make sense?