Yes, Bristol City are the franchise. Bristol City have played in the same place for well over 100 years. Unlike the 15ers who originally played in Eastville, then moved to a completely different city to play in Bath and then stole a rugby ground so they could play in Horfield. Oh and who were desperate to move out of Bristol to South Gloucestershire so that they could try and get a university to fund a stadium for them.
Yes, Bristol City are definitely the franchise.