Ah finally someone posts something pre Civil War.
The carriage is the Gribeauval design split trail model. In 1809 the US adopted the French system but still mounted their own calibers of barrels. The most common caliber during the War of 1812 was 6lber and I cant make a good estimation of that barrel itself from the angle the picture was taken.
The reason you saw something similar at Valley Forge is because the split trail carriage was at its height during the 1770s. A number of Gribeauval's first guns came over at Yorktown in 1781 or were shipped to the Cont. Army earlier in the war.
This is what it's supposed to look like:
This is a 6lber from New Orleans I believe. The lack of dolphin handles on your pic, leads me to believe the barrel came from another time period.
Wheels not matching was a logistical problem during the War of 1812 and the Napoleonic wars as a whole. There is tough an interesting anecdote about US artillery of the 1814 period that came from the British side on the Niagara frontier. They were under such accurate and organized fire that they told the Americans: "We mistook you for the French" (The French being the world reknown experts in this field at the time)
