Combine tomatoes, basil, olive oil, Pinot Gris, onion, garlic, salt, and black pepper together in a bowl; refrigerate until flavors blend, about 30 minutes.
Preheat oven to 400 degrees F (200 degrees C). Spray a rimmed baking sheet with cooking spray.
Place black cod, skin-side down, on the prepared baking sheet. Mix Dijon mustard and butter together in a small bowl.
Bake in the preheated oven for 5 minutes. Flip fish and brush mustard-butter over fish, coating the surface completely. Continue baking fish until it flakes easily with a fork, 5 to 6 minutes. Cut fish into 4 pieces.
Spread arugula onto serving plates. Arrange fish onto the arugula and top with tomato mixture and Parmesan cheese.