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Hi John
The simple answer is 19th century, maker unknown

. Now to what is known...
I have been researching these for some time. In the distant past, when authors felt they had to attribute everything to a factory that they had heard of, these were called Dorflinger, then Clichy, then 'Bohemian', depending upon what took the author's fancy. As far as I can see none of this was based on any form of hard evidence. I have also seen them called Saint-Louis, and 'unknown French factory'.
There is some eveidence to point us in the right direction though. The brass fittings on these doorknobs are all similar in style, and a few carry the word 'Brevet' , meaning patented. That has been taken by some to indicate that these are of French origin, whereas I would say it probably indicates that they were made in a Francophone country (not just France...).
Together with another European collector I have been investigating a varied group of antique paperweights that contain five-spoked 'starfish' canes (see short article in the Paperweight Collectors Circle Newsletter 111, April 2013). A couple of the weights in this group have canes that are near-identical to those in some of these doorknobs. We are preparing a major article about the group, but I can say here that the evidence is pointing to them being made in Belgium.
At the moment we cannot be certain where the doorknobs were made, but my strong suspicion is the French speaking part of Belgium (which had in Liège the glass makers Val St Lambert and Chênée amongst others). It may turn out that these are Chênée products, but that is speculation at present, and we need more research and more evidence.
Alan