Preheat a 6-quart air fryer to 400˚ F. Season the steaks with salt and pepper. Spray the air-fryer basket and grate insert with cooking spray and place the steaks in the basket. Cook the steaks until browned, 4 to 6 minutes; flip and cook 4 to 6 more minutes for medium rare. Transfer the steaks to a cutting board and tent with foil to keep warm. Wipe the air-fryer basket clean with a paper towel.
Reheat the air fryer to 400˚ F. Add the French fries to the air-fryer basket and cook until golden and crisp, 10 to 12 minutes. Season with salt.
Meanwhile, whisk together the olive oil, vinegar, mustard, thyme and 1/2 teaspoon each salt and pepper in a large bowl. Add the frisée and toss well to coat.
Slice the steaks and divide among plates along with the fries and salad. Sprinkle the steak and salad with chives and serve with ketchup and mayonnaise.