Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high heat. Season the fish with ¼ teaspoon each salt and pepper. Cook in batches until opaque throughout, 2 to 3 minutes per side.
Meanwhile, combine the carrots, almonds, vinegar, orange zest, the remaining ¼ cup of oil, and ¼ teaspoon each salt and pepper in a medium bowl.
Serve the carrot-almond dressing over the fish and spinach.