Combine first 11 ingredients in a small bowl; cover and chill until ready to serve.
Combine flour and next 3 ingredients in a shallow dish. Dredge fillets in flour mixture.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 2 fillets; cook 4 minutes on each side or until fish flakes easily when tested with a fork. Repeat procedure with remaining oil and fillets. Serve fish with tartar sauce. Garnish with fresh chives and lemon slices, if desired.
Note: Substitute baby dill pickles for the cornichons, if desired.