Most common problem with Fan shutting down at same time as burner is the 'time delay relay' being faulty (or blower circuit on newer circuit boards.
Also could be 'high temp limit switch' ......either because it is faulty OR most likely due to obstruction in airflow to/from furnace
Something blocking/obstructing RETURN air to furnace
OR
Furnace discharge blocked/obstructed....too many floor registers closed/blocked or duct work blocked (mouse nest/crushed duct)
Due to airflow issue....high limit switch shuts down firing but fan should still run.
Could be issue with BOTH
Easiest method..clear any obstructions and clean up connections on circuit board then fire it off again and check operation