In a bowl combine 6 tablespoons of the oil, fennel seeds, tarragon, lime peel, pepper, and salt. Stir well. Coat the tenderloin with seed mixture. Place meat on a non-reactive tray; cover loosely with foil. Refrigerate for 30 minutes or up to 1 hour.
Preheat oven to 425 degrees F. Place roast on a rack in a shallow roasting pan. Return any coating left on tray to meat. Insert an oven-safe meat thermometer into meat. In a bowl, toss together onions and 1 tablespoon of the remaining olive oil. Place onions on half of the roasting pan alongside meat. Roast, uncovered for 30 minutes. Meanwhile, toss together fennel and remaining oil. Stir onions and add fennel to other half of roasting pan alongside meat. Roast for 15 to 20 minutes more or until thermometer registers 135 degrees F for medium-rare doneness.
Remove roast from oven. Transfer roast to cutting board; cover with foil. Let stand 10 to 15 minutes (temperature should register 145 degrees F for medium-rare). Wrap roast tightly in plastic wrap; refrigerate until serving. Meanwhile transfer onions and fennel to separate bowls. Cover tightly; refrigerate until serving. Place roasting pan on stove top over low heat. Add red wine, stirring constantly to dissolve browned bits. Transfer sauce to bowl. Cover; refrigerate until serving.
To serve, cook green beans in a small amount of boiling salted water for about 5 minutes or until crisp-tender. Drain. Rinse with cold water until chilled; drain again. Toss green beans with reserved sauce. Arrange on platter. Slice tenderloin into thin slices and arrange on top of beans. Serve your tenderloin platter with roasted onion and fennel. Makes 12 appetizer or 8 main course servings.