Here are the photos of the carriage in its current state. The first thing to note is that it is upside down.
Picture 1. The square cut-out would be for one of the axle blocks. The large scallop cut-out would be either decorative or for weight reduction and was between the two axles along the bottom. The small block hanging on its side shows the cut-out for the trunnion on that side of the cannon.
Picture 3. The end of this side which would have had a matching axle block cut-out has gone but the the large scallop cut-out is there.
Picture 4. This is probably the front block with a scallop cut-out on which the barrel would rest at its lowest elevation.
I agree that it was probably a ship's cannon and to get a better idea of what it looked like (it's difficult to see detail on the postcard picture) take this link to an 1823 French ship's cannon.
french1823