Sprinkle gelatin over pineapple juice in medium saucepan; let stand 2 to 3 minutes. Cook over low heat, stirring constantly, until gelatin is dissolved. Cool to room temperature. Stir in champagne and nutmeg.
Freeze mixture in ice cream maker according to manufacturer's directions. Or pour mixture into 9-inch square baking pan and freeze until slushy, about 2 hours; spoon into bowl and beat until fluffy. Return to pan and freeze until firm, 6 hours or overnight.
To serve, place pineapple slices on dessert plates. Top each with a scoop of Pineapple-Champagne Ice. Garnish with mint.