The bread should of course be country-style French bread and the cheese Cantal or Laguiole. Gruyère or Emmenthal will not do and Parmesan will be too strong. Cheese wrapped in plastic is often too soft to grate. Cheddar would be the nearest English equivalent.
This soup will be more attractive if served in deep, individual ovenproof soup bowls as the top layer rises slightly and browns rather like a soufflé.