A319 flight crew reported a CFIT event during visual approach shortly after being assigned a late runway change. Flight crew utilized an INOP ILS as a visual backup guidance. Flight crew corrected low glidepath by following PAPI glidepath to a safe landing.

Narrative

Flying into ZZZ while on downwind we were changed from [Runway] XXR to [Runway] XXL. We reviewed the approach plate after inserting the new approach. On base to final after engaging the approach mode the aircraft kicked off the autopilot. The CA (Captain) hand flew the approach from that point forward. Initially we followed the ILS guidance but it appeared that the guidance was faulty as we noticed the glide slope and the localizer didn't appear to be giving accurate information. We had 15 kt. crosswinds. The ILS identifier was correct though. The CA acknowledged the poor ILS guidance and state he using the visual (PAPI) guidance as the weather was clear with no clouds. We were below a visual glide path but I do not recall the exact altitudes vs the distance from the airfield. We slowed the decent to pick up a normal visual glide path and about that time Tower advised us with a low altitude alert; which we already acknowledged internally. Once we picked up a normal glide path we resumed the decent and I eventually called out the 500 ft. stable call with a normal 800 ft. per minute decent so I 100% know we were stable at that point and don't remember the 1000 ft. AGL call as the aircraft did not enunciate either the 500 ft. or the 1000 ft. calls. Upon landing the Tower asked if we were using the ILS glide path. We stated initially but we soon disregarded it as it appeared to be faulty. They responded that ILS on XXL is NOTAMed out.The weather was clear but we knew we would experience a lot of turbulence in the decent. We had the Flight Attendants take their seats early. On the descent while on downwind it was bumpy with gusty winds. We got a late notice runway change but didn't mind as the weather was clear and [Runway] XXL was a longer runway. We briefed the approach but failed to review the NOTAMs for [Runway] XXL. As per company policy we back up visual approaches with glide slope to the maximum extent possible so we just planned on using the ILS as I was the quickest to set up. A review of the NOTAMs would have advised us the ILS was inop. Also the Tower could have advised us the ILS was out but we were on a visual approach. The Non working ILS giving us unreliable information distracted us until we disregarded the ILS info and just used visual references.It was an error of rushing and not reviewing all the information. We could have said no to the change; reviewed the NOTAMs properly; or asked approach if the glide slope and localizer where working.