Probably not. Franchising authority extends only to television. Municipalities aren't permitted (under federal law) to leverage their authority over the television side to regulate the broadband side.

I suspect the best thing municipalities can do is to make it easy to build competing systems. Take the list of concessions that Google Fiber cities made in return for getting service and commit to doing that for any potential entrant. Adopt one-touch make ready rules, maintain city-owned ducts in good shape and make it easy to get permits. Lay dark fiber every time the city digs things up to put in sewers or roads. Even a little bit of competition can have significant effects. E.g. in the D.C. metro area Comcast has no data caps because it's in competition with Verizon, RCN, and Cox. At the state level, municipal networks can provide a backstop for places (e.g. rural Maryland) that can't support sufficient private competition.