Spread the mustard on 6 pieces of the French toast. Divide the ham and turkey evenly among the 6 pieces and top each with 2 slices of the cheese. Spread the remaining pieces of French toast with the mayonnaise (if using) and sandwich together.
Heat a large skillet over medium heat. Spread 1/2 tablespoon of the butter on the top and bottom of each sandwich. Cook 3 sandwiches in the skillet until brown, 2 minutes per side. Transfer to a baking sheet. Repeat with the remaining sandwiches. Bake until the cheese is melted and the toast is heated through, about 4 minutes.