Sewing Tip: When sewing a french seam, it helps to trim the fabric raw edges by about 1/8" after the first stitch but before flipping the layers over to enclose the edges. This additional excess removal will prevent any fraying threads form getting caught in the final seam and will also eliminate some bulk in the finished application.
As reminder, when completing a french seam, the fabric layers are flipped over the seam allowance layers to encase their raw edges. During this process, the raw edges continue to fray and they sit too close to the final seamline, these threads will get caught in the final seam stitch and show on the right side of the finished seam.
If you trim the seam allowance edges slightly after the first stitch application, the raw edges will naturally sit farther way from the finished seam stitch which provides less risk for the raw edges to get caught in the finished seam. If you take a closer look at the image above, you can see the raw edges of the seam allowance (between the two fabric layers) aligning at about 1/8" away from the seam stitch. Thanks to this alignment, when flipping the seam to its right side, there should be no threads or raw edges peeking through.