Make the Algerian Sauce: In a bowl, combine mayonnaise, ketchup, tomato paste, harissa, cilantro, red onion, and lemon juice. Stir until creamy and smooth. Chill until ready to use.
Make the Cheese Sauce: In a saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1–2 minutes. Slowly pour in the half and half, whisking constantly. Once it thickens, add the cheddar and gruyere and stir until melted. Mix in crème fraîche, mustard powder, cayenne, nutmeg, salt, and black pepper. Keep warm.
Marinate the Chicken: In a bowl, combine yogurt, tomato paste, olive oil, harissa, salt, coriander, oregano, smoked paprika, garlic, black pepper, and lemon juice. Add the chopped chicken and mix well. You can cook it right away or marinate for at least 1 hour or even overnight.
Cook the Chicken: Heat a sauté pan over medium-high heat. Add the marinated chicken and cook, stirring occasionally, until fully cooked and slightly charred, about 6–8 minutes.
Assemble the Wraps:
Lay a tortilla flat. Spoon a layer of cheese sauce down the center, then pile on the cooked chicken. Add a handful of hot, crispy fries right on top. Drizzle with Algerian sauce. Tuck in the sides, fold the bottom up, and roll into a rectangular-ish shape, seam-side down.
Lightly spray the press with oil. Place the wrap diagonally, press until golden, then rotate 90° to create that criss-cross grill pattern. Slice in half and enjoy right away, with extra cheese sauce or Algerian sauce on the side.