Preheat an oven to 450. Line a baking sheet with parchment.
Toss the potatoes, olive oil, salt, cumin and cayenne together until the potatoes are evenly coated. Spread on a baking sheet and bake for 30 minutes or until crispy.
Dipping sauce: In a small mixing bowl, whisk together the avocado, mayonnaise, horseradish and spices until smooth. Serve with fries.