If my memory is correct "Lefaucheux" was a Frenchman. He is quite often thought of in connection with Pinfire guns as well as this style of double guns. It is highly unlikely with it having the Parker name on it along with the Belgian proofs that Mr Lefaucheux himself had any part in building it, they were quite popular it some parts for a number of years & built my other makers.
Is there a key passing through the forend, the bbls may simply be keyed to the forend.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra