Heat milk over medium-high heat in a heavy saucepan to 180° or until tiny bubbles form around edge (do not boil). Remove from heat.
Combine sugar and cornstarch in a medium heavy saucepan; add milk, stirring with a whisk. Cook over medium heat 4 minutes or until thick, stirring constantly.
Gradually add hot milk mixture to egg in a bowl, stirring constantly with a whisk. Return milk mixture to pan. Cook over medium-low heat 6 minutes or until thick, stirring constantly. Remove from heat. Pour into a bowl; stir in vanilla. Cover surface with plastic wrap; chill.
Stir champagne into chilled custard, and serve with raspberries and nectarines.