A300 pilot reported receiving an ECAM message GREEN RSVR LO LEVEL in cruise. After troubleshooting and discussing options the crew continued to destination airport and made a safe landing.

Narrative

Approximately 450 miles from ZZZ; ECAM message: GREEN RSVR LO LEVEL. Crew confirmed validity of message on overhead panel and on HYD Systems Page.Crew Complied with ECAM Actions:GREEN PUMP 1 OFF GREEN PUMP 2 OFFBRK - A/SKID ALTN/ON(At this time; no additional procedural steps displayed on ECAM; and PITCH FEEL 1 and SPLR 6 lights NOT illuminated) Note: ECAM indications cycled continually during remainder of flight.Crew reviewed QRH and AOM for additional information. (Crew noted that PROC: L/G GRAVITY EXTENSION was a requirement with Green System failure which was NOT displayed on ECAM). Crew observed HYD Pressure on HYD SYSTEMS Page continually cycling from approximately 2;400 psi to 0 psi. Crew transferred aircraft control to Captain. Crew established ACARS comm with company and unsuccessfully attempted voice comm. Crew established phone patch with company on ARINC and requested communication with System Matter Expert (SME). Communication with SME was not successful due to poor reception. Crew reverted back to ACARS comm with Company. Note: Eventually additional procedural step displayed on ECAM for: L/G GRAVITY EXTENSION in addition to PITCH FEEL 1 and SPLR 6 lights on overhead panel. Crew discussed situation and plan of action which would include Gravity Extension of Gear. Crew elected to request hold at 12;000 ft. approximately 25 miles from ZZZ airport in order to complete all checklists; brief approach; compute landing distance; consider fuel remaining and potential Go-Around; discuss brake usage during landing roll; and to configure aircraft early due to anticipated slow movement of slats/flaps. Crew elected to request priority handling; anticipating the possibility of having to stop on the runway. Crew elected to start APU during hold; anticipating shutting down engines following landing to allow towing of aircraft to ramp.ILS Approach and landing to Runway X ZZZ was uneventful and crew was able to clear the runway following landing. Crew established comm with fire/rescue crew. Fire Crew reported smoke coming from #2 Engine. With no additional fire indications in cockpit; crew elected to shut down the #2 Engine. Fire crew reported smoke subsided. Crew established comm with ZZZ Maintenance staff and then shut down #1 engine. ZZZ Maintenance staff directed crew to pull the #2 Fire Handle; without actuating fire bottles. Aircraft was towed to ramp.