See how much the fleece stretches where you want to add the cotton. If it stretches a lot, add a row of stay stitching to the fleece edge before trying to sew the cotton to it. You might also be able to attach the cotton to the less stretchy edge of the fleece with an overlock stitch like you would use on a t-shirt. If all else fails, consider ironing a nice edge on the cotton, place it on top of the fleece and do an appliqué buttonhole stitch?