Toss the fries with 1 teaspoon of the paprika. Lay out in a single layer on a baking sheet and bake until crispy, about 30 minutes.
Sprinkle the steak with 1 teaspoon salt and 1/2 teaspoon pepper. Heat 1/2 tablespoon of the oil in a large skillet over medium-high heat until very hot. Add the steak and cook, flipping once, until brown on both sides and cooked to desired doneness, 4 to 5 minutes per side for medium-rare. Transfer to a cutting board (reserve the skillet) and let rest 5 minutes.
Add 1/4 cup water and the remaining 1/2 teaspoon paprika to the skillet and boil over medium-high heat, scraping up any brown bits, until slightly reduced, about 30 seconds. Remove from the heat stir in the mustard, vinegar, soy sauce, Worcestershire and the remaining 2 tablespoons oil.
Thinly slice the steak against the grain. Pour any accumulated juices into the skillet with the vinaigrette in the skillet. Toss the arugula and vinaigrette together in a large bowl. Season with salt and pepper. Divide the salad, steak and French fries among 4 plates.
Copyright 2016 Television Food Network, G.P. All rights reserved.