Burner cycling on then off/back on/off is called 'limiting' which is when the airflow has been restricted and heat exchanger high temp limit switch is opening (too hot) then fan continues to run so temp drops...high temp limit switch closes and burner lights back off
You have something obstructing/blocking either the furnace discharge air flow OR the return air to furnace
Could be closed/blocked register, could be crushed ductwork, could be how/where stuff is stored
Fan runs cause high temp limit switch opened.burner keeps firing back off cause thermostat temp set point has not been met....high temp limit switch controlling burner shutting down/relighting