Prepare fries: Preheat oven to 425°F. Cut each potato in half crosswise. Cut each half into 1/2-inch slices, then cut slices into 1/2-inch strips (to resemble French fries). Place potatoes in a large bowl.
In a small bowl, combine paprika, cumin and oregano. Drizzle oil over potatoes. Using a silicone spatula, toss potatoes gently yet thoroughly to coat. Sprinkle paprika mixture evenly over potatoes and toss gently.
Arrange potatoes in a thin layer on a large, foil-lined baking sheet. Bake for 25 to 30 minutes, stirring every 10 minutes, until tender and golden brown.
Meanwhile, prepare dipping sauce: In a separate small bowl, whisk together all sauce ingredients and refrigerate until serving.
Remove potatoes from oven, sprinkle evenly with salt and serve with dipping sauce.