What was found
Enroute to BDL @ approx. 270fl, A&B fire loop on #1 engine came on. Engine fire lights came on and fire bell. Bell silenced, #1 engine shutdown per procedures. Alt fire bottle discharged, light remained in handle, Main bottle discharged light remained on. Fuel dumped, returned to BQN, landed normal. Red fire handle light remained on thru landing and taxi to gate.Corrective Action: Inspected and found A loop engine gear case sensor (loop) shorted. R&R'd loop I/A/W 26-11-01. Replaced engine firex bottles. Run up Engine checks satisfactory. Aircraft returned to service.