Sorry, I did not completely understand your question then. Of course, you can try to set cookie's domain to different domain, like in your case - if you have englishdomain.com, you can set cookie for frenchdomain.com. But it won't work, for sure. Because server itself handles this setting automatically. In cookie function, in most cases (like miniBB's default), you can even have no value for domain at all. No, it is impossible and can not be possible, I've already explained why.
This setting is necessary for people having trouble with automatic cookie recognition, or need some advanced possibilities. And its purpose is for READING only, not writing.