If I were using a French seam on a garment I would sew this slightly differently around the corners. However, as this is a bag and it needs to be a bit stronger on the corners this method will suffice.
Place the bag with the wrong sides together and pin around the main bag, leaving the handles free and unpinned.
Sew with a 6mm seam allowance along the three sides of the bag.
If the seams are a little bulky you can trim the seam allowance down to 4mm.
Trim the excess fabric across the corners.
Turn the bag out so the seams are on the inside. Roll the seams to the edge and press flat.
Pin to enclose the first seam and sew a second seam 8mm wide, enclosing the first one.
Turn the bag around the right way again. Roll the seam so it sits on the edge and press the seam flat as before.
Match up the handles of the bag with the wrong sides together. Sew a 6mm seam allowance.
Press the seam to one side. Fold the bag with the right sides together to enclose the first seam. Sew another seam 8mm wide. Press the seam to one side.