Cut out 4 (12- x 16-inch) pieces parchment paper, and place on a baking sheet. Blanch fennel and carrot in boiling water 4 minutes. Drain and rinse with cold water.
Divide fennel and carrot evenly among parchment pieces. Place 1 salmon fillet on each, then top with lemon, capers, and chives. Drizzle each with wine and olive oil; sprinkle with sea salt and pepper. Fold parchment to enclose salmon; twist ends to secure.
Bake at 400° for 14 to 16 minutes or until cooked through. Salmon should be slightly translucent in center.