It is an oenophile's real-estate fantasy: decamp to Bordeaux and find a way to spruce up an old château.

Yet many luxury home-hunters who have managed to buy in this exclusive wine region, where vineyards can go for over $63,000 an acre, soon discover an unexpected complication. Aside from renovations or vine maintenance, new owners often find themselves also overseeing a wine team—a small staff of locals to do everything from…