Organic French Tarragon
Artemisia dracunculus
Tarragon is a perennial, it grows well in Northern Europe, but needs a little love and care here in the South of France.
French Tarragon can only be reproduced through root splitting in early Spring. Planting Tarragon seeds results in Russian Tarragon which is very light in flavour, and in my opinion not worth while growing.
So to start with you either need to buy a plant from a certified organic source, or find a friend who gardens organically.
Reproducing Tarragon is simple. Every Winter French Tarragon dies back, and each Spring it pushes out new shoots. 
Wait until these new shoots are about one centimeter high. At this point, with a trowel or garden folk, lift the entire plant out. I grow my mother plants in half barrels to make it easier to lift the entire plant out without damaging the roots. What you should get is a bouquet of shoot emanating from the root base.
Have a look at the outside shoots, with your fingers firmly pinch the base of the shoot as near to the root base as you can. If you can find a side shoot with a sub shoot coming of it perfect, if not don’t worry. Gently pull the shoot from the base. Ideally it will come away with a few roots. Do this as many times as you wish, but be careful to leave about half of the central shoots so the plants continues to thrive. With the separated shoots, bury them up to their necks, or in this case their green tips, in a rich cutting medium, like Orgasyl; water and never let dry out. I get around a 90% success rate doing this.
When you start to see secondary shoots emerging, plant in larger pots or even in the ground. Though my advice the first year is to continue in a pot. My experience is that if French Taragon makes it through to it’s first Spring they are good for 8 to 10 years.
Planting on and growing
French Tarragon likes a neutral soil,ph 6.5, though it can tolerate some alkaline, 7.5 max. It likes a rich well drained spot, ideally with a touch of shade at the height of the day. Because I lift all my mother plants up, I refresh the soil around them every year. If they are in the ground a covering or organic material every Autumn after they die back is a good idea, as the worms pull the material underground over Winter, and it can also protect the sleeping plants from any hard frosts. If you are planting in the ground leave a 50cms space around them to let them reach their full potential size. Takes about two years for this to happen. They do like to be watered every week or so in Summer.
If you are planting them in a pot, find one at least 30 cms deep and the same across, larger helps. Plants in smaller pots risk being killed by hard frosts, and it is difficult to refresh the soil as they tend to get pot bound quickly.
Companion planting,
Tarragon is widely believed to be good at keeping parasitical insects at bay, it could be psychological because of its strong aroma. It is suppose to be a good companion for Aubergines
(For more on Companion planting see https://en.wikipedia.org/wiki/List_of_companion_plants)
Harvesting French Tarragon.
You can start harvesting the top leaves in late Spring, once it has got over 10cm or so high. The tips are best cut with a sharp clean blade rather than pinched.
The leaves dry well, though I find they guard their colour better, which makes them more attractive to eat if you pop them in a brown paper bag which you have punched a few holes in hung in a dry, but shaded spot.
Tarragon can also be used to flavour vinegar. Here in France they pickle gherkins, cornichons, in vinegar with Tarragon leaves.
Cooking with Tarragon
The strong aniseed flavour is wonderful with chicken, indeed stuffing the skin of a chicken with Tarragon flavoured butter before roasting, and then making a cream sauce with the drippings is one of my favourite summer dishes. I sprinkle freshly cut Tarragon leaves in the sauce at the end just to make it extra strong.
Mixing with home made mayonnaise it is an lovely topping for boiled eggs.
Salmon with a Tarragon cream sauce is also a firm favourite here at the Domaine de Montrouch
Check here for some ideas on using Tarragon in cooking http://www.bbc.co.uk/food/tarragon