Combine garlic, 2 tablespoons chives, 2 tablespoons parsley, olive oil, and 1/4 teaspoon salt. Rub on both sides of snapper fillets; cover and chill.
Heat butter in a large saucepan over medium heat; cook leeks in butter 5 minutes, stirring occasionally. Add potatoes, fennel, and wine. Increase heat to medium- high; cover and simmer 5 minutes. Add chicken broth and remaining 3/4 teaspoon salt. Bring to a boil; cover, reduce heat, and simmer 15 to 20 minutes or until potatoes are tender. Remove from heat, and gently stir in lemon juice and remaining 2 tablespoons each of chives and parsley. Set aside, and keep warm.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Make 2 diagonal cuts through skin (but not flesh) of each fillet. Add fillets, skin side down, one at a time, to skillet. Cook 4 minutes; turn and cook an additional 4 minutes or until fish flakes easily when tested with a fork.
Divide each fillet into 3 portions. Spoon ragoût evenly among 4 bowls; top each bowl with a portion of fillet. Garnish with fennel leaves, if desired.