Step 1: Sew the first seam with wrong sides together. For a 5/8" seam allowance, sew the first line of stitches 2/8" (1/4") from raw edge.
Step 2: Flip the fabric so that rights sides are together. Press.
Step 3: With right sides still together, sew second line of stitches 3/8" from pressed edge, enclosing raw edges from first seam. This will use up the full 5/8" seam allowance (2/8" + 3/8" = 5/8").
Step 4: Press the seam open and you're done! For a faux flat-felled seam look, you can also sew a third line of stitches attaching the french seam to the garment.