Staying in an actual castle in the Loire valley.

There are quite a few chateaux ( usually smaller ones) in the Loire that are now hotels. You can google them. We stayed at the Chateau de Pray near Amboise- it's quite small, but charming, and with a Michelin star restaurant. I'm not aware of any of the grand chateaux ( those that have daily paid openings) that also rent out rooms.

There is a chateaux owner association where owners have b and bs in their historical chateaux. Look for Bienvenue Chateaux web site. One of my favorites is Domaine Bidaudieres in Vouvray. The grounds are lovely for a walk. All of these lodging choices will require a car.

There is hôtel IN the grounds at Chambord, the relais de Chambord. Many rooms have close up views of the Château. The hotel itself is a contemporary remodelling of old buildings, very tasteful. It is not cheap, of course, but not outrageous either (highly seasonal).

An instagrammer I follow is staying at the Chateau des Arpentis near Amboise, and it looks like it might fit the bill.

There are several loose associations of chateaux owners who rent out as hotels -- you can find them on line. I would suggest looking at pictures of the rooms as well as house and grounds when choosing. I once booked a castle north of Paris for my family and while the castle looked lovely at a distance our rooms looked like bog standard holiday inn rooms and not the romantic old rustic castle we hoped for.