Preheat oven to 425º. On a baking sheet, arrange fries in a single layer. Bake fries until golden and crisp, about 25 minutes.
Meanwhile, season steak with 1 teaspoon salt and 1/4 teaspoon pepper. In a large cast-iron or heavy skillet over medium-high heat, heat 1 tablespoon oil. Cook steak, flipping halfway through, until browned on both sides and medium-rare, 5 to 7 minutes per side. Let rest 10 minutes.
In a skillet, add 1 tbsp and cut + add shallot over medium heat, stirring occasionally, until shallot softens and is translucent, 1 to 2 minutes.
Add vinegar and cook, scraping browned bits from bottom of pan, until reduced by half, 2 to 3 minutes. Remove skillet from heat and pour vinegar mixture into a medium heatproof bowl. Whisk in lemon juice, mustard, and 1/4 teaspoon salt. Whisking constantly, slowly pour in remaining 4 tablespoons oil; season with salt and pepper.
Thinly slice steak against the grain. Divide cucumber, arugula, tomato, steak, and fries among plates. Sprinkle with blue cheese and drizzle dressing over.
