I was watching that item, and was a bit puzzled by it. Old English is a strong possibility. I had ruled out French - I could not tie the canes to any particular factory - but was toying with the thought it might just be Belgian.
I have had a couple of weights that were similar, and the canes had similar structure. One looked like a cut down bottle stopper. They both came from sources in the Birmingham area, so on balance I would vote for an English origin, from one of the less well known and as yet unidentified factories.
I assume your paperweight is made of lead glass? What is the base finish like?