Preheat a panini press or griddle while you prepare the ingredients, then cut the French bread into 12 even slices.
Spread about 1 tablespoon of butter on one side of each bread slice and place six slices butter-side down on the hot panini press or griddle.
Spread honey mustard on the inside of each bread slice, if using.
Divide the turkey, thin apple slices, and cheddar evenly among the six bottom bread slices, keeping the layers even so the sandwiches press cleanly.
Top each sandwich with a remaining bread slice, butter-side facing up, and close the panini press.
Grill for 3 to 5 minutes, until the bread is evenly golden and crisp and the cheddar is fully melted.
If using a griddle, flip each sandwich carefully halfway through cooking and press gently with a heavy skillet for even browning.
Let the sandwiches rest for 1 minute, then cut them in half and serve immediately.