Soak the potatoes in enough cold water to cover, stir in 2 tablespoons vinegar and place in the fridge for at least 1 hour and up to 4 hours. When you refrigerate the potatoes, the starch will turn to sugar which is a good contrast to the vinegar in this recipe.
Heat a large Dutch oven with 3 inches of oil to 325 degrees F.
Strain the potatoes from the water and pat them completely dry. Cooking in batches, fry the potatoes in the hot oil, moving the fries with a spider or slotted spoon to keep them from sticking to each other, until the potatoes are softened and very light golden brown, about 4 minutes.
Remove the fries onto a cooking rack and raise the oil temperature to 375 degrees F. Fry a second time until the fries are golden brown all over, 2 to 3 more minutes. Toss with the remaining 2 tablespoons vinegar, season with salt and serve.