Trim beef tenderloin. Place meat in a large bowl. Pour Red Wine Marinade and refrigerate covered, for several hours or one day, turning occasionally.
Remove meat from marinade and pat dry. Prepare grill and place rack 4 – 6 inches (10 – 15 cm from fire. Oil rack lightly and place beef tenderloin. Grill meat, turning frequently to brown all sides. Cook until the desired doneness.
Remove meat from grill and place over a warm platter. Cover with aluminum foil for 10 minutes and let meat rest.
Cut the tenderloin into slices (¾ – 1 inch / 2 – 2.5 cm) and top each serving with a slice of tarragon butter.
Red Wine Marinade:
Combine all ingredients. Pour mixture over beef tenderloin and cover.
Combine butter, fresh and dry tarragon, parsley, lemon juice, salt and pepper in a medium size bowl. Beat with a wooden spoon until smooth. Form butter mixture into a cylinder (4 inches / 10 cm) and wrap in plastic film. Chill until firm.
Cut into slices (3/4 – 1 inch / 2 – 2.5 cm) and serve 1 slice over each tenderloin. Remove.