Slice potato paper-thin on a mandoline. Dissolve salt in the hot water; add potato. Soak until water cools completely, about 20 minutes.
Heat 2 inches oil in large heavy-bottom pot until 350 degrees on an instant-read thermometer. drain potato slices; pat dry. Fry in batches until crispy but still purple, about 1 minute. Transfer to a paper-towel-lined plate. When cool, top each with 1/4 teaspoon creme fraiche and 1/4 teaspoon caviar. Serve immediately.