Trane XE80 Furnace fan won't stop running
So the furnace heats, but when it's time for the furnace to cycle down, the burners go OFF, but the blower stays ON?
Are you certain the Fan switch on the thermostat is turned to AUTO?
You can try removing the Green thermostat wire. This controls the fan. If the fan goes OFF after you remove the green wire, then you probably have a bad thermostat, or fault thermostat wiring.
If not, and if this furnace is controlled by a circuit board, then you could just have a bad board. Only way to troubleshoot that would be to have a tech analyze it, or to replace it with a known good board.