Cut the potatoes into fries, then soak in a bowl of cold water for 1 hour to remove excess starch and prevent discoloration.
Fill a large pot with at least 6 inches (15 cm) of canola oil. Heat over medium-high heat until the oil temperature reaches 325˚F (160˚C).
Dry the potatoes thoroughly with paper towels.
Working in batches, fry the fries in the hot oil for about 5 minutes, or until light golden brown. Transfer the fries with a slotted spoon to a rack to drain and season with salt.
Increase the oil temperature to 375˚F (190˚C).
Add the fries back to the oil in batches and fry until golden brown, about 3-5 minutes. Transfer the fries with a slotted spoon back to the rack to drain again. Season with 1½ tablespoons of Fiery spice blend.
In a small bowl, combine the mayonnaise, remaining ½ tablespoon of Fiery spice blend, and the lime juice. Whisk to combine.