In a medium bowl, combine mayonnaise, French dressing, and sweet pickle relish.
Add white vinegar to the mixture and stir well.
Incorporate the onion powder and garlic powder, mixing until smooth.
Add sugar, salt, black pepper, and paprika to the bowl.
Stir all ingredients until fully blended and creamy.
Taste the sauce and adjust seasoning if necessary.
Cover the bowl with plastic wrap or a lid.
Refrigerate the sauce for at least 30 minutes to allow flavors to meld.
Serve the sauce as a topping for burgers or fries.
Store any leftovers in an airtight container in the refrigerator.