Wash and scrub potatoes under cold running water. Pat dry with paper towels. Cut in half lengthwise, then into long strips about 1/4-inch thick.
In a deep pot or deep-fat fryer, heat about 3 inches of oil until a thermometer reads 250 degrees. Line a metal tray or baking sheet with paper towels.
Add one handful of the potatoes to the pot. Fry until tender but have no color. Remove with a slotted spoon. Drain on the paper towels. Repeat the procedure until all the strips are cooked. Refrigerate until cool.
Reheat the oil to 350 degrees. Line the metal tray with fresh paper towels.
Add the cooled potatoes a few handfuls at a time and fry until golden and crispy. Remove with a slotted spoon. Drain on the paper towels. Toss with the tarragon, parsley and salt while the slices are still hot. Serve immediately.