In a mixing bowl, whisk together flour and eggs. Gradually add in milk and water, stirring to combine. Add salt and butter; beat until smooth.
Heat a lightly oiled skillet over medium-high heat. Pour or scoop the batter onto the skillet, using approximately ¼ cup for each crepe. Tilt the pan with a circular motion so that the batter coats the surface evenly.
Cook the crepe for about 2 minutes, until the bottom is light brown. Loosen with a spatula, turn and cook the other side. Keep crepes warm.
In another bowl, combine the chicken, apple, cheese, mayonnaise, mustard, salt, and pepper.
Fill each crepe with the chicken mixture. Fold and serve warm.