Preheat an oven or an air fryer to 400°F.
Arrange French fries in a single layer on a large rimmed baking sheet or in air fryer basket. Bake them in preheated oven according to the time shown on package, or according to air fryer instructions.
Place butter in a 2-quart saucepan over medium heat, cooking until melted and bubbly. Whisk in the flour to combine, then cook for about 2 minutes, until mixture is thick and pasty.
Gradually whisk in milk, about 1/2 cup at a time, stirring well in between additions to create a smooth sauce. Add salt, pepper, ranch powder, and 1/4 teaspoon cayenne powder, then stir to combine.
Reduce burner heat to medium-low and continue cooking, stirring frequently, for about 5 minutes, until the sauce is thick enough to cling to the back of a spoon.
Using a silicone spoon, gently stir in shredded cheese to combine. Continue cooking, stirring occasionally, for 2-3 minutes, until Cajun cheese sauce is thick and creamy. Remove from the heat and set aside until the French fries are ready.
When French fries are cooked through and golden brown, transfer them to a serving platter. Pour the Cajun ranch cheese sauce evenly over them, then sprinkle remaining 1/4 teaspoon cayenne evenly over the top. Serve while warm.