B&B or Bed & Breakfast are rather common terms.
They are typically a room in a residence or former residence turned small hotel. The proprietor is typically the owner. And, as the name suggests you get a bed and breakfast for the price.
In AmE, B&Bs are typically very quaint places found in rustic locations. If you look rather hard, can find a Bed & Breakfast in a major city, but major hotel chains tend to dominate there. But, because of the identity with rustic locales, it carries the notion of a "romantic getaway".
You would typically not bring children or family to a B&B.
A small hotel with inexpensive rooms of varying quality is known as a motel. A portmanteau of motor and hotel. The notion is a hotel for motorists which requires no reservations. You would bring children or families to a motel.
Motels have a wide variation in quality from "seedy" (meaning a place to pick-up prostitutes and hide out from the police) to polished, clean, but inexpensive national chains.
The two French terms you mentioned have no currency in AmE. Table d'hôte has largely been replaced by terms like Chef's table for the original sense of a "host's table". Or prix fixe menu in the more modern sense.