Move the oven rack to the middle position. Preheat the oven to 425°F.
Slice the French bread so it opens horizontally. Lay the French bread on a rimmed cookie sheet.
Layer the provolone, Swiss, and pepper Jack over one side of the bread and the meats over the other side of the bread. Bake for 5 minutes until the cheese is melted and the meat is warm.
In a bowl, add shredded lettuce, sliced red onion, pepperoncini, mayonnaise, Italian dressing, red wine vinegar, Dijon mustard, minced garlic, salt, and pepper. Toss to combine.
Remove the sandwich from the oven. On the cheese side, add a generous layer of the prepared toppings. Then, layer the sliced tomatoes and sprinkle with salt and pepper. Sprinkle the meat side with grated Parmesan.
Close the sandwich. Cut into 4 subs and serve immediately.