Remove wing tips from chicken wings and discard; cut remaining wings apart at the joints.
Heat several inches of oil in a deep-fryer to 375°F. Fry chicken in several batches until golden brown and no longer pink inside. Drain on paper towels. Cook French fries in hot oil until crisp and golden brown. Drain on paper towels.
Meanwhile, melt butter in a small saucepan over low heat. Stir in all remaining ingredients and mix well; heat through. Place chicken in a large bowl or pan and drizzle with warm sauce; toss until evenly coated.
To serve, mound French fries on plates and top with chicken wings. Serve with blue cheese dressing and celery sticks, if desired.
Makes 6 servings.