Slice potatoes into thin strips for fries. Soak in cold water for 30 minutes, then drain and pat dry.
Pound chicken breasts to even thickness. Marinate in buttermilk for at least 15 minutes.
In a shallow dish, mix flour, paprika, garlic powder, salt, and pepper. Dredge each chicken breast in flour mixture, pressing to adhere.
Heat 1/2 inch oil in a large skillet to 350°F. Fry chicken for 4-5 minutes per side until golden and cooked through (internal temp 165°F). Drain on paper towels.
For fries, heat oil to 375°F. Fry potatoes in batches until golden, about 4-5 minutes. Drain and season with salt.
Toast buns. Spread mayonnaise on bottom buns, top with chicken, pickles, and bun tops. Serve with fries.
Tips
For extra crispy chicken, double-dip in buttermilk and flour.
Fries can be baked at 425°F for 25 minutes if preferred.
Store leftover chicken and fries separately in the refrigerator for up to 2 days.