Beat eggs in a bowl until smooth. Add buttermilk, almond extract, cinnamon, and nutmeg and beat well until batter is smooth. Dip bread into batter until evenly coated.

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Spray a skillet with cooking spray and heat over medium heat. Cook coated bread until golden brown, 4 to 5 minutes per side.

Combine white sugar, water, and brown sugar in a saucepan; bring to a boil and cook for 1 minute. Remove saucepan from heat and cool syrup for 2 minutes. Stir maple-flavored extract and vanilla extract into syrup. Serve syrup over French toast.