Preheat the oven to 425°F. Line a large rimmed baking sheet with parchment.
In a small bowl, stir together 1 tablespoon of the olive oil, the paprika, coriander, and lemon zest and juice; set aside.
In a medium bowl, toss the potatoes with 1½ teaspoons of the olive oil, ¼ teaspoon of the salt, and ⅛ teaspoon of the pepper. Arrange the potatoes on one side of the sheet pan, being careful not to crowd the pieces. Roast for 15 minutes.
In the same bowl, toss the asparagus with the remaining 1½ teaspoons olive oil, ¼ teaspoon of the salt, and ⅛ teaspoon of the pepper.
Remove the pan from the oven. Stir the potatoes. Place the salmon fillets opposite the potatoes. Brush the seasoned olive oil mixture over the tops and sides of the fillets. Season with the remaining ¼ teaspoon salt and ¼ teaspoon pepper. Add the asparagus to the pan between the salmon and the potatoes. Roast until the potatoes are browned and crisp, asparagus is tender, and the salmon is cooked through, 10 to 12 minutes.