A320 Captain reported course deviations due to FMGC failure resulted in critical equipment failure requiring ATC guidance.

Narrative

During cruise portion of STAR; an ECAM message appeared Nav Fm/gpc pos disagree. Within seconds ATC queried if we were direct ZZZZZ; 20 deg right of course. Captain NAV showed direct; FO; showed right of course. Ran ECAM checklist; but ECAM went away. About 5-10 mins later; ATC once again asked if we're direct ZZZZZ; he was showing us right of course. From that point on we were given headings to fly. After arrival; MX (Maintenance) indicated there was a problem with the FMGC and that it needed to be replaced.