Podewils, you are right in your assumption. Those fold-down European peep sights were indeed only intended as an optical device to sharpen up the images of target, front- and rear sight!
Your buttplate is indeed not made of plastic, but of heat-pressed horn or,at best hard rubber called "Ebonite". The double grip Lefaucheux action, as patented in 1836, was the continental European standard action during the second half of the 19th century, but went out of use on rifles with the advent of smokeless. As I have yet to see a continental single-bite Lefaucheux action, I believe this to be a British simplification. Perhaps Mr. Joseph Lang, who made a copy of a Lefaucheux pinfire after seing on e at the Crystal Palace Exhibition, did not fully understand the importance of the original double bite.
Does your rifle have any BUG proofmarks under the barrels? If not, it was made and sold before April 1, 1893, the day the proof law became effective.