Because linen does ravel a good bit you might be hesitant to try turn under appliqué with it. I use the freezer paper/starch method with all appliqué but it works especially well with linen. In case you are unfamiliar i'll briefly describe.
Flip your pattern over on a light box and trace the appliqué piece in reverse onto the dull side of freezer paper. Cut out on the traced line. Iron the paper to the backside of your fabric. NOTE: On most fabrics you would use an eighth inch measurement but with linen make it almost a quarter inch.
Cut out fabric piece a scant quarter inch beyond the paper edge. Spray some starch into a small plastic cup and with a paint brush (I use my finger) brush the starch onto the wrong side of the extended quarter inch of fabric. With your fingers press the starched edge to the back, over the edge of the paper all the way around. Press with hot iron. Remove paper and press. For more detailed information and photos check the internet. Best appliqué method i have found.
This little bear is part of a new pattern design. He has a few friends I think you are going to like. More soon!