Put the French bread or ciabatta bread halves in the oven on a baking sheet at about 350°F (175°C) or under the broiler or grill for five minutes or until they are beginning to take on a bit of colour.
Meanwhile, mix the crab meat with the mustard, red pepper, and celery.
Add crème fraîche or sour cream as well as salt and pepper to taste. Mix together gently.
Divide the crab mixture between the pieces of bread and top with the cheese slices.
Return the crab and cheese topped bread to the oven for five to ten minutes, or place under the broiler or grill, until the cheese is bubbling and brown.
The cheese gets very hot, so allow these to cool a bit before serving one half of the panini or ciabatta to each person, or cutting into small pieces to serve as hors d’oeuvres.