This was so embarrassing.
I bought this plant because it had a little sign in it saying that it was french tarragon. When it continued to grow the second year I should have known something was wrong.
A friend came over this year and said is that Rosemary. After he left I took a good look at it and my rosemary plant and guess what...yep it's rosemary not tarragon. I feel like such a naive person. And I didn't even buy it at Wal-mart this was at a nursery.