Stir to combine the chives, dill, creme fraiche, cream cheese, salt and pepper in a medium bowl.
Wash the radishes in cold water, and then thinly slice them on a mandoline into a medium bowl of ice water. Let them sit for 5 minutes, and then drain and place on a towel to dry.
To assemble the sandwiches, spread 1 to 2 tablespoons of the herb cream cheese over the slices of bread. Top with the smoked salmon, another tablespoon of herb cream cheese, sliced radishes and a sprig of dill.