Try one of these:

Richters
Horizon Herbs
Nichols Garden Nursery

FataMorgana

I live in Baton Rouge and have gotten French Tarragon from Jim Mizelle, he has a nursery and comes to the farmer's market in Baton Rouge and New Orleans. I forgot where the nursery is, but I can look into it for you. French tarragon usually dies out here in the summer due to the heat, so I always grow Mexican Marigold to cover the summer. I have had luck with Spanish Tarragon through a summer.

Forgot about Google, Hope this helps

Here is a link that might be useful: Mizell Farms

Where is that FAQ?? .. Maybe RICHTERS should run an ad here!

I have some to trade. 3 or 4 inch pots, first year plants.

Lynn

I got my French taragon by buying a bunch of the herb at the supermarket and rooting it in water. I did this in May ( don't know if the season made a difference) and every cutting rooted. I now have over two dozen plants. You might do the same. I simply cut each stem to about four inches, removed the leaves that would otherwise be submerged, and they shortly rooted. Good luck.

That is the only way true French Tarragon can be propagated. There are no viable seeds. Only thing is, you have to pinch off a leaf and really smell it to see if its a fake or the real thing. The fake (Mexican or Russian), looks almost the same but its smell is almost none and taste is not much either, more like a grass..