Combine champagne, sugar, and lemon rind and juice in a large saucepan; stir well. Bring to a boil. Reduce heat to low; simmer 5 minutes.
Beat yolks in a small mixing bowl. Gradually stir one-fourth of hot mixture into yolks; add to remaining hot mixture, stirring constantly. Cook over medium heat, stirring constantly, until thickened. Ladle into individual soup bowls; serve warm as a dessert soup.