To prepare mussels, combine first 9 ingredients in a small bowl; set aside.
Bring wine and clam juice to a boil in a Dutch oven. Add mussels; cover and cook 2 minutes or until shells open. Remove mussels from pan with a slotted spoon; discard any unopened shells. Keep warm.
Bring wine mixture to a boil over high heat; cook until reduced to 1/3 cup (about 15 minutes). Pour liquid over mussels. Add the cornichon mixture; toss.