Preheat oven to 350°F.
Cut French bread into 1-inch cubes.
In a medium mixing bowl, beat yolks and 1 1/4 cups sugar.
In a pan, heat milk, remaining sugar, heavy cream and vanilla extract over medium heat, whisking constantly. As mixture begins to boil, turn down heat.
Add 1/2 cup of milk mixture to egg mixture in bowl and whisk well (This brings temperature of yolks up so that they won't curdle.)
Add egg mixture to rest of pan mixture. Stir 5 - 7 minutes.
Stir in white chocolate until smooth.
Pour mixture over bread. Let set 4 hours, to make sure liquid soaks into bread.
Place bread in buttered 10 x 12 x 2-inch baking pan. Cover with layer of plastic food service film (Important - See Note Below).
Then top with foil.
Place baking pan inside larger pan. Pour in water into larger pan to come up halfway around sides of bread-filled pan.
Place in oven and bake 45 minutes.
Remove from oven and cool on the counter.