No your furnace fan should not run constantly after the heating cycle is done.
Your furnace fan should run only when the heating cycle is in operation and once the heating cycle is over the furnace blower should shut off along with the heat.
The problem could be that your furnace fan is set to auto. If it is set to auto on your thermostat then you should turn the fan setting to off.
There could other problems such a high temperature switch that is bad causing your furnace fan to keep running constantly.
If you can't find the problem yourself you might want to hire an HVAC company to come out and check the problem.