2004 cadillac deville code 306also states fuel system fault cl which means?

Question

car misfires at idle does not seem to misfie beyond 800 rpm

Answer 1

P0306 Misfire number 6 cylinder

When a engine has a misfire that particulat cylinder does not contribute , at a higher RPM the engine does seem to even out , even with this event the misfire is still there but not noticable, You will need to remove the sparkplug on number 6 to determine the cause  it can be from the sparkplug ,to sparkplug wire to a mechanical condition.