Beat the French vanilla pudding mix and cold milk with an electric mixer for about 2 minutes, until thickened.
Add the sour cream and mix until smooth. Fold or beat in the thawed whipped topping on low speed until evenly combined.
Arrange a layer of vanilla wafers across the bottom of a 9-by-13-inch glass dish. Top with half of the sliced bananas and half of the pudding mixture.
Repeat with another layer of wafers, the remaining bananas, and the remaining pudding mixture.
Crush a few extra vanilla wafers and sprinkle the crumbs over the top. Cover and refrigerate overnight, or for at least 8 hours, before serving.