In a medium bowl combine mayonnaise, sour cream, paprika, onion powder, garlic powder, and salt. Add the mixture to a squeeze bottle if you have one.
Add the chicken into a greased 9×13 inch baking dish. Pour the bbq sauce over the chicken and bake for 1 hour at 400 degrees F, flipping halfway through. Shred the chicken using two forks.
Meanwhile, cook frozen French fries according to package directions. Place the cook fries onto a baking sheet. Spoon the bbq chicken over the fries and cover with cheese