Air carrier Captain reported a failure of the Autopilot during an autoland approach. Flight crew returned for a normal approach and landing.

Narrative

During a redeye (last leg of 5 day trip) I decided that it would be a good idea to practice a CATII autoland into ZZZ since the conditions were VMC; winds calm; low traffic volume; and good braking action was expected. This was also a precaution against any unexpected symptoms of fatigue since this flight was a redeye. That being said; I felt very alert and well rested for the flight; and the FO (First Officer) showed no signs of fatigue. I briefed the approach and covered items from the CATII approach briefing guide in the company publication. We informed ATC of our intention to do an autoland during the arrival; and they acknowledged our intent; as did Tower. The approach was picked up via radar vectors; as briefed; and we configured on time to quickly establish stabilized approach criteria with no issue (fully configured and finishing deceleration to VAPP above 1;000ft AGL). At approximately XA:03 and 1500ft AGL; we received the ECAM warning that the Autopilot had failed. I announced that I had the field in sight; we were stable; and could continue following the flight directors. I followed my flight directors and checked on the sight picture of the runway. I saw three red lights on the PAPI as expected since the ILS glidepath was not coincident with the PAPI. I continued on the flight directors until I heard the GLIDESLOPE warning; looked up and saw 4 red lights on the PAPI; then executed a Go-Around. The Go-Around was completed without issue; and I successfully re-engaged the Autopilot after level-off. I rebriefed the approach as a CATI hand flown approach; and we continued to a stabilized approach and landing without issue. The Autopilot appeared to fail due to a momentary onboard computer failure as indicated on a post flight maintenance print out.Lessons Learned: After the level-off; the FO informed me that the aircraft reverted to vertical speed (-1;000 FPM) when the Autopilot failed and thats why why we got low on the glideslope as the aircraft finished decelerating to VAPP; even though we were following the flight directors. The lesson here is to keep the FMAs (Flight Mode Annunciators) in your scan to verify what the Fight Directors are guiding you towards. If I had seen that the underlying approach was lost; I would have executed a Go-Around earlier.