In a mixing bowl, whisk together milk and French vanilla pudding until no lumps remain. In the bowl of a mixer, combine the cream cheese and condensed milk together and beat until smooth. Fold the whipped topping into the cream cheese mixture. Add the cream cheese mixture to the pudding and stir until blended. Pour the mixture over the cookies and bananas and cover with the remaining bag of Chessmen.. Refrigerate for at least a couple of hours before serving.