In a medium bowl, whisk together 1 cup mayonnaise, ¼ cup French dressing, 2 tablespoons sweet pickle relish, 1 teaspoon white wine vinegar, ½ teaspoon paprika, ¼ teaspoon garlic powder, and ¼ teaspoon onion powder until smooth. Refrigerate the sauce while preparing the salad.
In a large skillet over medium-high heat, brown 1 pound lean ground beef.
Season the beef with 1 teaspoon salt and ½ teaspoon pepper while cooking.
Continue cooking the beef for 7–10 minutes until fully browned and cooked through.
Transfer the cooked beef to a paper towel-lined plate to cool slightly.
Chop 3 heads romaine lettuce and divide evenly among serving bowls.
Top the lettuce with the cooled ground beef, 1 thinly sliced red onion, ½ cup halved cherry tomatoes, 1 cup shredded cheddar cheese, and ½ cup diced dill pickles.
Drizzle the prepared Big Mac sauce over each salad before serving.