Preheat the oven to 350 degrees F. Put a 1/4-inch layer of salt in the bottom of a small baking dish. Place the beets on top of the salt, making sure they are not touching each other. Cover the beets with the remaining salt (save some for seasoning) and bake until fork-tender, about 1 hour, 15 minutes. Remove the beets from the salt and let cool to room temperature.
Meanwhile, make the dressing: Puree the goat cheese, creme fraiche, olive oil, vinegar and shallot in a blender until smooth. Season with salt and pepper. Refrigerate until ready to use.
Heat the vegetable oil in a small skillet over medium heat until shimmering. Add the sage leaves and fry until crisp, 5 to 10 seconds. Transfer with a slotted spoon to a paper towel-lined plate to drain; season lightly with salt.
Peel the beets (the skins will slip right off) and slice into thin rounds using a mandoline or sharp knife. Divide the beet slices among plates. Spoon some of the goat cheese dressing on top. Put the arugula in a bowl, drizzle with the lemon juice and olive oil, season with salt and toss. Add the arugula salad to the plates; drizzle with more goat cheese dressing, if desired. Top with the pine nuts and fried sage.