I don't think so. Most franchises are challenging enough for a highly motivated, completely focused owner to operate. Plus they are expensive to get into, require constant attention, and are difficult to exit. If running a franchise is not the primary focus of the owner, chances are it will not be successful. Plus, I doubt whether most franchisors would even allow this structure.

If the primary motivation for the question is create job skills for clients of the non-profit, then the non-profit would be much better off by reaching out to businesses in its locale and developing a training program that would place clients in those businesses.