Heat oven to 400 degrees. Combine capers, peppercorns, dill seed, and lemon juice in a small bowl. Set aside.
Fold two 24-inch lengths of parchment paper in half crosswise, cut into a half-heart shape, and open. On one half of one piece, arrange a quarter of the fennel slices 2 to 3 inches from the fold. Sprinkle a quarter of the peppercorn mixture and a quarter of the chopped dill on top; place one piece of fish over the fennel, and sprinkle with salt. Layer with another quarter of fennel slices, peppercorn mixture, and chopped dill.
Fold the other half of parchment along the crease, covering the ingredients. Make small overlapping folds to seal the edges, starting at the top of the heart.
Two inches from the end, twist the parchment twice, gently but firmly, to seal. The paper will puff during cooking, so make sure the seams are tightly sealed. Repeat process to make the second packet.
Place packets on a baking sheet; bake for 12 to 15 minutes. Remove from oven, open packets, and serve immediately.