Combine first 5 ingredients in a shallow bowl.
Rub salmon with brown sugar mixture. Place fillets, skin-side down, on grill rack coated with cooking spray. Grill over medium-high heat (350° to 400°) 12 minutes or until desired degree of doneness. Remove skin and discard.
Toss spinach with 1/3 cup Peach Dressing. Arrange spinach on individual serving plates, top with salmon, and drizzle with remaining dressing.