Preheat a grill to medium high. Prepare the french fries as the label directs; keep warm.
Form the beef into four 6-ounce patties, about 3/4 inch thick; press the center of each patty with your thumb to make a 1/2-inch-deep indentation. Season the patties on both sides with salt and pepper. Lightly brush the grill grates with the vegetable oil, then grill the patties, indentation-side up, until marked on the bottom, about 5 minutes. Flip and cook until marked and slightly firm, about 3 more minutes for medium doneness. During the last minute of grilling, top each patty with a slice of cheese. Remove the patties to a plate and let rest 5 minutes. Grill the buns, cut-side down, until lightly toasted, about 1 minute.
Spread the bun bottoms with ketchup and top with the burger patties and french fries. Cover with the bun tops.