One of the largest surviving medieval buildings, bigger than any cathedral, is one you don't hear much about: the papal palace at Avignon, now in southern France.
Construction of a palace on the site began in 1252, for a bishop. In 1309, Pope Clement V, alias Raymond Bertrand de Goth, one of my favorite medieval names, fled the chaotic violence that had broken out in Rome after his election and accepted the protection of the King of France at Avignon. (Avignon belonged to the papacy but was within what we would call the French sphere of influence.) Popes had often resided outside of Rome, but Clement moved the whole papal curia to Avignon with him, all 300 secretaries, judges, cardinals, etc.
Clement lived in a monastery and the courtiers made do with the old bishop's quarters until 1334, when newly elected Benedict XII razed the old bishop's palace and began building the new one. The architect was Pierre Poisson of Mirepoix. But the curia was expanding rapidly – it reached 2,000 personnel by the end of the century – and Benedict's huge building was too small by the time it was finished. So other popes immediately began enlarging it, completing what became known as the New Palace (directly above) by 1364.
The completed palace measured 11,000 square meters, or about 3 acres. Above is the main courtyard, known as the Cour d'honneur. Imagine it full of elegantly dressed churchmen, walking about in small groups, muttering conspiratorally to their companions as they nod politely to others, trying to extract messages from who was nodding how deeply to whom.
Drawing of late medieval Avignon by Etienne Matellange, variously dated by sketchy internet sources to the 1400s or 1500s.
View from the river below. Wikipedia describes this location as the "impregnable rock of Doms", but consider what Alexander the Great or Julius Caesar would have made of the statement that this or any fortress was "impregnable" and then resolve never to use that locution again.
In 1377 the pope moved back to Rome, but he died and dueling conclaves elected two popes to replace him, one holding court at Rome and one at Avignon; we call this the Great Schism, although it wasn't particularly great. (Compare, say, the split between Catholic and Eastern Orthodox, 970 years old and counting.) Until 1417 there were two popes, or even three, but they finally sorted it out and when there was one pope again he lived at Rome. The Avignon palace was mostly abandoned.
Which explains why it is such a great remnant of the middle ages; nobody who used it after 1417 had the money to do anything to the building but let it molder. It was completely stripped of furniture, of course, but the building remains, with its tile floors
and frescoes on the walls and ceilings; these are the building's treasures today.
The south of France remains high on my list of places to visit, so perhaps I will even see this one day.