Susie,
I truly don't know the answer. My success with it has been 100% due to dumb luck.
My guess is that French Tarragon likes somewhat sandy or silty soil, not too rich in humus - as do thyme, rosemary, and artemisia. I understand that it is not happy in heavy clay. And one source recommends that if you garden on dense clay you grow it in a container. From what other people say it sounds like giving it some shade in Phoenix is an excellent idea. I could imagine, though, that it might really like a few hours of morning or late afternoon sun. Here in Prescott mine grows happily in full sun. When I grew it in NJ it seemed to do well in poor, dry, silty soil in direct sunlight. But it died quickly when I tried to move it.
http://www.bonnieplants.com/Le...
