Clean the carrots and cut into sticks. Melt the butter and fry the carrots in it. Remove. Sweat the flour in the remaining butter and deglaze with milk. Bring to the boil and continue to simmer briefly. Season to taste with salt, pepper, sugar and lemon juice. Add finely chopped tarragon and let it steep briefly (do not boil anymore). Season to taste with the mustard. Add the carrots again and heat them up in the sauce.
Note on tarragon: There are French and Russian ones. The Russian is more common, but has almost no flavor. The French, on the other hand, has the full aroma of tarragon. When I buy tarragon, I try a small rolling paper.