Some suitable alternatives to tarragon are chervil, fennel seed and aniseed. Chervil, like tarragon, is an herb often used in French cooking. It has lacy, pale green leaves similar to carrot tops. Chervil has a delicate, anise-like flavor and is a staple ingredient in Bearnaise sauce recipes.
Fennel seed is from the fennel plant, which has a pleasant anise aroma and taste. The dried seeds also have medicinal properties. Anise is a plant grown in the warm climate off the Mediterranean and the Middle East. The seeds have a lovely, sweet smell and give meals a hint of licorice flavor.