If other forms of potato, e.g. baked potatoes, mashed potatoes, also cause problems, you are likely allergic or intolerant to potatoes. Get yourself tested to be sure and avoid eating potatoes. However, if only french fries trigger stomach pain, it might be either overeating or the high oil content of the food. Such oily foods can cause stomach pain if you already have a problem in your digestive system, like gallbladder inflammation or pancreatitis. If the pain is sharp and severe, you might need immediate medical help, otherwise visit a gastroenterologist to find the exact cause.