- Neither can my sister. - My sister neither. (informal) - My sister can't either. - My sister can't as well. (not sure about how formal/natural/common this actually is)
Yes. "French is not the private property of French people, nor English of English people" might not cause any confusion. One can easily read it the same meaning with "French is not the private property of French people, nor is English the private property of English people".
I think the above is correct English. See: ----- 'What caused his wrath to be directed towards me especially, I cannot tell, nor can my sister,' said Philip, looking full at his uncle; 'but I seem to have come in for a full share of it.'