Combine preserves and mustard in a small bowl; stir with a whisk. Spread 1 side of each bread slice with 2 teaspoons mustard mixture. Place bread slices, mustard mixture side up, on a baking sheet coated with cooking spray.
Heat a large skillet over medium-high heat. Coat pan with cooking spray. Add apple and onion to pan; cook 3 minutes or until tender, stirring occasionally. Add spinach; cook 1 minute or until spinach begins to wilt. Layer each of 4 bread slices with 1/4 cup spinach mixture, 1/2 cup chicken, and 1 cheese slice. Place sandwiches on a baking sheet coated with cooking spray; broil 1 1/2 minutes or until cheese is bubbly. Remove from heat, and serve immediately.