Peel potatoes. Slice into steak-sized wedges. Place potatoes in a large bowl. Cover with cold water. Soak for at least 1 hour.
Heat 1/2 inch of oil in a heavy bottomed pan over medium-high heat.
Drain the potatoes and pat them dry with paper towels. Fry the potatoes until golden brown on both sides. Remove to a wire rack.
Make the cheese sauce: Melt butter in a saucepan over medium heat. Stir in the flour and cook until bubbling, about 1 minute. Pour in the milk. Bring to a boil. Reduce heat to low and whisk in the cheddar until smooth.
Place the fries in a large bowl. Add the Cajun seasoning and toss until fries are coated. Transfer fries to a serving plate. Drizzle with cheese sauce and ranch dressing. Garnish with chopped chives, if desired.