Set oven to 350°F (175°C) and butter or spray a 9x13-inch baking dish.
Add cubed French bread to a large bowl. In another bowl, whisk together milk, heavy cream, eggs, both sugars, vanilla, cinnamon, nutmeg, and salt until smooth.
Pour the custard over the bread. Gently fold to coat every piece. Let sit for 15–20 minutes so the bread soaks it up.
Stir in raisins, if using. Pour mixture into the prepared baking dish. Drizzle melted butter evenly over the top.
Bake for 45–50 minutes, until golden and set in the center. A knife should come out clean but the pudding should still be moist.
While it bakes, melt butter in a saucepan over medium heat. Whisk in cream and brown sugar until dissolved. Stir in bourbon and simmer for 2–3 minutes to thicken. Remove from heat and add vanilla.