Pieper was a Belgian gun maker for a long time, from well before World War 1 until at least 1940. They made good guns, but they were a step down in prestige from FN, which was a newer firm that made top-of-the-line products. Pieper was more like Buick or Chevy compared to FN's Cadillac.
Pieper made a wide variety of guns, and in sizable numbers, but they never became well known in the United States. I am only familiar with their pistols, not their long guns. The gun you have looks like a style of 22 rifle that was very popular in Europe before and after WWI.
Bayard was the name of a famous knight, and was Pieper's trademark. Some people use Bayard as a model name, but I think Pieper used it on all their guns.
Sorry I have nothing more specific to your gun; it seems to be in decent shape for its age. That's not that common for inexpensive 22's.
Oh, and thanks for putting up good pictures. That will help people tell you what they know.