Heat oven to 400° F. Place the fish on one side of four 12- to 15-inch lengths of parchment.
Season the fish with ½ teaspoon salt and ¼ teaspoon pepper. Top with thyme and orange slices.
Fold the parchment over the fish; make small overlapping folds along the edges to seal. Transfer to 2 baking sheets and bake for 12 minutes.
Meanwhile, heat the oil in a large skillet over medium-high heat. Add the spinach, basil, and ¼ teaspoon each salt and pepper. Cook, tossing, until just wilted, 2 to 3 minutes.
Carefully cut the packets open and serve with the spinach.