Local government would run the fibre network and terminate everything to a central POP (or several). They're responsible to maintain the physical network and ensure every connection can obtain the minimum speed and latency standard. This could even be cable/DSL/wireless, so long as the minimum speed is hit. They can contract this out, but it's largely irrelevant to the consumer.
At the POP is where ISPs take over and provide the upstream connection to the actual internet, and this is who the consumer pays. The ISPs can compete based on whatever combination of price, speed, transfer limits and/or add-on services they choose.