Renting a chateau in France is not the same thing as renting a castle in Scotland or renting a castello in Italy. And the difference is not only geographical. Although, along with castillo in Spain, the words are usually used as translations for each other, and are derived from the same Latin root, they refer to different types of property altogether.
Whereas an English castle is a very specific type of building, originally a fortified residence for a feudal lord, usually substantial in size and instantly recognizable by its (usually) crenellated towers, a French chateau is not simply a castle in France. Although French chateau is the literal translation for English castle, the term is in fact applied far more broadly, and can in practice mean any old or grand country house. In French, the specific term chateau fort is used for a castle of the medieval, fortified kind. What distinguishes a French chateau is that that it is a grand residence in the countryside as opposed to a town, the word palais standing for its urban equivalent. Again, this differs from English in that a palace in England, Scotland, Wales or Ireland is just as likely to be found in the countryside.
As far as someone looking for a holiday rental is concerned, the significant difference is less likely to be social, historical or architectural, interesting though those aspects are, but one of price. A bona fide castle for rent in England, Scotland, Wales or Ireland is reasonably to cost upwards of twenty thousand pounds for a week's exclusive use, whereas you can hire a chateau in France for as little as 3,000 euros per week, although it is likely to be what would be called in England a country house or even a farmhouse.
Since medieval castles were originally the stronghold of the local lord, their size would reflect his power and the extent of his authority, from small buildings that amount to little more than fortified farmsteads, to great fortress bastions that dominate the country for miles around. Just as these lords were even distributed all over the British Isles and France, so too were the seats and symbols of their power. Yet very few of these genuinely medieval buildings survive, and the vast majority of castles, chateaux and country houses for renting date from the 17th and 18th centuries, and occasionally even later.
Regarding the location of these later chateaux and country houses, a marked difference evolved in practice between France on the one hand and England, Scotland, Wales and Ireland on the other. In the latter, the grand country houses of the aristocracy (still sometimes called castles although they no longer served a military purpose) were still dotted even about the land, as they represented their owners' local pre-eminence, although their supremacy was now social rather than political, so castles rentals in Scotland for example, or country homes to rent in England can be found almost everywhere.
However, in France local social pre-eminence was simply not worth having – all meaningful ambition was focused on the King and the Court at Versailles, both for the aristocracy and the newly rich bourgeoisie who followed them. As such, a chateau for rent in France is more likely to be found in the center rather than the periphery, in the Loire Valley, Normandy, Burgundy and the Dordogne.
In Italy, the situation is different again. As in Great Britain, a castello (castle) is a medieval or renaissance military stronghold. The equivalent of renting a country house here is hiring a villa. The urban equivalent of the country house (more similar to France in this respect) is the palazzo, although that term also includes the fortified residences of the merchant princes of the renaissance Italian city states. Unlike in France, though, it is possible to find villa rentals in Italy almost everywhere in the peninsula – it is not so much a question, as in England, of the weight of local interests anticipating over the gravity of central authority, but rather that there was no central authority at all, Italy being until the mid-nineteenth century a patchwork of a dozen or more independent states. As a consequence, you can find a castello or Italian villa to rent anywhere from Sicily to Tuscany to the Veneto.