- Cannot be adjacent to another Château.
The Château is a weak and underwhelming tile improvement, for a multitude of reasons. First, it is one of the last unique improvements to be unlocked in the game, yet its yields and effects do not reflect that. Second, it cannot be adjacent to another Château. This restriction also means that the dream of surrounding a wonder completely with 6 Châteaux can never be achieved. Just compare it to the Persian Pairidaeza, another Culture-generating improvement that can be unlocked three eras earlier, and you can really see how weak the Château is. In terms of usage, you should only build this next to a wonder, since only the wonder adjacency aspect of the Château scales into the late game. A bare minimum Château built without a wonder nearby is a waste of real estate and a Builder Charge. Only 1 extra Gold from every adjacent Luxury Resource and 2 if adjacent to a river, at this point, is also too minor to be prioritized.
If one must ask, one cannot afford it. A château is a manor house or country home of landed gentry, usually without fortifications. In the Middle Ages, a château was largely self-sufficient, being supported by the lord's demesne (hereditary lands). In the 1600s, the wealthy and aristocratic French lords dotted the countryside with elegant, luxuriant, architecturally refined mansions such as the Château de Maisons. But many of these stately homes were burned during peasant revolts and populist revolutions. But a few remain as tourist attractions. Today, the term château is loosely used; for instance, it is common for any winery or inn, no matter how humble, to prefix its name with "Château."