From what I can tell, the "French-design" cannon is actually a hybrid design. I don't think the Koreans made an exact copy of a French cannon, but made their own design styled after captured pieces. I have heard that there were some captured 1866 cannon, but also there may have been other French cannon that were taken off a shipwreck in 1847.
The Koreans, after facing Western forces twice (1866 and 1871), wanted to upgrade their artillery from the ancient styles they had to that point. So, the "Daewongun" (the regent of Korea and father of the king) ordered such cannons be developed; the result was the 1874 design. The extant cannon came from a palace and also from an old fortress. I believe the carriages may not be original (I could be wrong), but may be copies of the originals.