If you are going to run a franchise league, please:
(a) Learn the history of the franchises
(b) Make sure that all teams in the league legitimately comply with those histories

There is a great (pinned) thread at the top of this page that provides detail on the most common mistakes.  The definitive source for what constitutes a franchise is www.baseball-reference.com if you have any questions.

This link in particular is vital:
http://www.baseball-reference.com/teams/

I am posting this because I am currently in a league where an owner has a team with players from both the Cleveland Spiders (1890s NL team, now defunct) and the Blues/Naps (1900s AL team which later becomes the modern-day Indians).  These are absolutely not part of the same franchise, but it's an easy mistake to make, and it's the commissioner's job to be on top of this stuff.