Grease a 9x13 inch baking dish. Spread the cubed French bread in the dish.
In a medium bowl, whisk together the eggs, milk, sugar, 1 teaspoon vanilla, cinnamon, and nutmeg. Pour the mixture over the French bread cubes. Cover the dish and refrigerate overnight, or for at least 8 hours.
Preheat oven to 350 degrees F (175 degrees C).
In a medium bowl, beat together the softened cream cheese, 1/2 cup sugar, and 1/2 teaspoon of vanilla until light and fluffy. Spread the cream cheese mixture over the bread cubes evenly.
In a small bowl, combine the brown sugar, flour, and 1 teaspoon of cinnamon. Pour the melted butter over the top and stir until combined. Sprinkle the topping over the cream cheese layer.
Bake uncovered for 35 to 40 minutes, or until the top is golden brown.