For applique, I have found for neat edges, sew seam of fusible fabric to the right side of the fabric, sewing all the way around. Snip a slit in the fusible, pull through to reverse the piece, smoothing out the edges.
TWO ways on sewing these two pieces together... sew so the non-fusible side is RST. When you turn and iron, the fabric will be firm...OR...sew so the fusible side is RST. When you turn and iron, the fabric is attached to the square. Your choice to make here.
This way, the edges are smooth and then you can applique as you choose.