Working in two batches, place the pineapple and ginger root inside your blender or bowl if using a hand blender. Pulse until the pineapple and ginger are pureed.

Pour the pineapple mixture to a fine mesh strainer placed over a large bowl. Use a spatula to press the mixture through the sieve. Transfer the strained juice to a large punch bowl or pitcher.

Stir the rum, orange juice, and simple syrup into the pineapple mixture. Refrigerate until ready to serve.

When ready to serve, gently pour the champagne into the punch bowl and give the mixture a stir. Garnish with frozen pineapple rings if desired.