you have to create two column per page on master page and thread the left column on the left page with left column on the right page and do the same with the right columns.
in this way you have two different stories in your document and the footnotes will be independent
I believe I couldn't make my point clearly. Problem is styling but not numbering. I want to differentiate the footnote style for each language if there is a way.
Thanks again for your interest.
How a bout to apply to any language footnote a different paragraph style?
I don't think you can do this with a paragraph style directly, since as the OP notes document footnote options are global, and I'm not even sure it's possible with Find/Change since the global options assign a paragraph style, and part of that style includes a language declaration, making it impossible to find text with a different language assigned so you could change the paragraph style or assign a character style.
Yes, as far as the formatting goes for the footnote's representation itself, length of graphic line, color of graphic line, distance to text etc.pp., all that kind of formatting is global per document or even global per InDesign book file if the footnotes need to be synchronized between the documents.
The only way out I could think of is a workaround that requires at least two documents (or three documents). One for the one language, a different one for the other language where e.g. all two documents' pages are placed into a third document and assembled this way. Page by page and constantly updated, if changes are made in the two source documents for the languages.