Heat oven to 425°F. In medium bowl, mix beaten eggs and egg white, the milk, rum extract and nutmeg until well blended.
Dip bread slices into egg mixture, coating both sides well. Place in ungreased 11x7-inch (2-quart) glass baking dish, place bread slices. Pour remaining egg mixture over bread slices. Let stand at room temperature 10 minutes.
Spray cookie sheet with cooking spray. Remove bread slices from dish; place on cookie sheet. Bake 12 to 15 minutes or until golden brown, turning slices once halfway through baking.
Meanwhile, in 1-quart saucepan, mix syrup ingredients; cook over medium-low heat, stirring occasionally, until cranberry sauce and sugar have melted. Serve French toast with syrup.