Heat the oven to 425 degrees F. Line a baking sheet with a large piece of foil, then place beets on top. Drizzle over enough olive oil to coat, then season with salt and pepper. Wrap the edges of the foil around the beets, crimping the edges securely to make a foil packet. Roast for 10 minutes.
Meanwhile, in a jar, combine the red wine vinegar, sherry vinegar, mustard, and 1 cup olive oil. Season with salt and pepper and shake to combine.
After 10 minutes of beets roasting, remove the baking sheet from the oven. Place a sheet of parchment paper on the baking sheet next to the foil packet. Place the salmon fillets on the parchment, and season with salt and pepper. Drizzle 1 to 2 tablespoons of the mustard vinaigrette on the salmon, and return the baking sheet to the oven. If your baking sheet seems overcrowded, place the beets or salmon on an additional one. Roast until the beets are fork-tender (you can pierce them through the foil), and the salmon is cooked through, 12 to 15 minutes.
When the foil packet is cool enough to touch, open it, and place the radicchio over the beets to wilt slightly. Drizzle over a few tablespoons of mustard vinaigrette and toss to coat.
Break the salmon into pieces on serving plates and scatter the beets and radicchio around. Top with additional dressing, salt, and pepper as needed.