Bring a large pot of water to a boil and add a large pinch of salt. Add the tagliarini and cook until al dente. Drain the pasta, reserving about 1/2 cup of the cooking water.
In a large, deep skillet, melt the butter over moderate heat. When the foam subsides, add the minced shallot and cook over moderately low heat for 2 minutes, stirring. Add the crème fraîche, parsley and tarragon. Stir in about 1/4 cup of the reserved pasta cooking water and season with pepper. Add the pasta and smoked salmon ribbons and toss well. Add up to 2 more tablespoons of the reserved cooking water if the pasta seems too dry. Remove from the heat. Add three-fourths of the caviar and toss gently. Serve in shallow bowls, garnished with the remaining caviar.