Preheat the oven to 425°F.
Fold each square of parchment paper in half to crease it. Spread it out flat on a work surface and rub one side of each sheet with olive oil.
Place 1 fish fillet in the middle of each oiled side. Sprinkle the fillets with some of the paprika, salt, and pepper to taste.
Place some of the shredded vegetables on top of each piece of fish.
Sprinkle the fresh herbs over the top of the vegetables. Sprinkle all over again with more paprika and salt and pepper to taste.
Drizzle about 2 teaspoons of olive oil lightly over each.
Fold the second half of the parchment over the fish and vegetables. Beginning on one side, fold the edge over. Repeat, folding it a second time to seal the edge well. Repeat for the other sides. Follow the process with the remaining fillets.
Place the parchment packets on a baking sheet. Bake in the oven for about 15 minutes, until they are puffed. Serve the fish and vegetables in the paper immediately. Slice a big x in the top of the paper, and peel it back.