Heat oil in a large nonstick skillet over medium-high heat. Pat scallops dry with a paper towel. Add scallops to pan; cook 3 minutes on each side or until done. Remove from pan; keep warm.
Add mushrooms and shallots to pan; sauté 3 minutes or until liquid evaporates and mushrooms darken. Stir in Champagne, mustard, salt, and tarragon, scraping pan to loosen browned bits. Remove from heat; stir in sour cream. Serve with scallops.