French Tarragon is an unusual plant that has many benefits when grown. Tarragon is one perennial plant that cannot be grown from a seed. It is a plant that grows around 12 to 24 inches high with long stems that have leaves in a dark green color. You can only grow tarragon from a cutting of another plant. French Tarragon needs to be planted in the sun, but also needs some shade. It grows best in well-drained loose packed soil. It does not grow very well in wet or tightly packed soil.