Cut the lemon, blood orange, and naval orange into halves. Cut 1 half into slices and juice the other half of each.
Whisk lemon juice, blood orange juice, and navel orange juice together in a bowl with the brown sugar until dissolved.
Season salmon fillets with salt, pepper, and garlic salt. Poke holes into each fillet about 2 inches apart using a fork. Place salmon in a resealable plastic bag and pour juice marinade into bag; coat with the marinade, squeeze out excess air, and seal the bag. Marinate salmon in the refrigerator, at least 1 hour.
Preheat oven to 400 degrees F (200 degrees C).
Place salmon, skin-side down, into a baking dish. Drizzle marinade and champagne over salmon and sprinkle with dill. Arrange lemon, blood orange, and navel orange slices over salmon.
Bake in the preheated oven until salmon is cooked through and flakes easily with a fork, about 20 minutes.