Heat a large skillet over medium-high heat. Cook and stir beef and onion in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Stir barbeque sauce into ground beef mixture and simmer until heated through, about 5 minutes.
Preheat quesadilla maker or preheat oven to 350 degrees F (175 degrees C)
Spread 1/2 the ground beef mixture onto a tortilla and top with 1/2 the Cheddar cheese and 1/2 the French-fried onions; top with a second tortilla. Repeat with remaining ingredients.
Cook each quesadilla in quesadilla maker or on a baking sheet in preheated oven until golden brown and cheese is melted, 5 to 10 minutes.
