Translating taxonomy list name for a custom link in rewrite result field
How can I achieve this? There's no translatable field for this view that I can add and use as variable.


Really?!? If you have a representative node of the category content (with the proper language set) you should be able to have a relationship to that nodes language settings, and also the url path to nodes' url path for say, French, in this case.

There's no token support to Rewrite the link in Views to the path with X language setting for the node? .... eg, under Replacement Tokens for the field there's no configurable token for like, node:path:lang:YOUR-LANG or something similar -- I typically dont do internation sites, but i'm 99% sure this type of flexability comes out of the box.