Gently toss together the chuck and sirloin in a large bowl, making sure not to overwork the mixture. Form the beef into four 3/4-inch-thick patties, each about 4 inches in diameter. Sprinkle evenly with 1 1/2 teaspoons salt and 1/2 teaspoon pepper.
Lightly grease the grill grates. Put the patties on the grill; do not press down on them with a spatula. Cook until the patties are seared and browned on one side, about 3 1/2 minutes. Flip and cook on the second side until browned, about 3 minutes for medium-rare.
Assemble the burgers using your favorite buns and toppings and serve with french fries, if desired.
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