Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.

Place French bread in a large bowl. Pour heavy cream over bread and let soak. Add sugar, eggs, and vanilla extract; mix all together with your hands. Add white chocolate chips and mix thoroughly.

Bake in the preheated oven until bubbly, 40 to 45 minutes.

While bread pudding is baking, prepare the sauce. Combine white chocolate chips and heavy cream in a small saucepan over low heat. Cook, stirring constantly, until melted. Drizzle a small amount of sauce over each serving.