A French dart is a bust dart coming from the side seam pointing upwards, it is not a straight dart but it is shaped one.
This is an example of a French dart sewn in a linen blouse.( you see the inside of course)
Sewing a French dart is not difficult but needs a bit of extra care due to the way the dart is placed because the dart is not on the straight of grain lengthwise or crosswise, it can stretch during sewing and handling like pressing. The dart needs a reinforcing to stay in shape.
A way to prevent stretching this French dart out of shape is to add a lightweight piece of stay-tape to the stitch line.
If you do not have the light weight polyester stay-tape you can also use a piece of lining cut at the cross or lengthwise grain or cut a bias cut piece of lining which you steam press and stretch during the pressing so it will not grow anymore.The advantage of using a bias cut lining it will not fray, like a crosswise or straight of grain will do.
Place the tape for reinforcing the dart at one of the dart stitching lines and sew the dart from the widest point (side seam) towards the end.I did placed the stay tape at the seam allowance which is the one heading towards the center front.
The next step is pressing the dart open till about ½ inch (1 cm) from the top, the point can be pressed open by using a toothpick which you can insert at the point, press the last ½ inch with the toothpick inside the point over a pressing ham or the end of the ironing board.
It will depend if the garment will be lined or not and what kind of fabric you use to decide how the seams are going to be finished.
For example if your garment is a blouse or dress and will be unlined and your fabric is a light to medium weight you can finish the seams by serging both seam allowances together.Press the dart downwards.
If your garment will be lined no finishing is needed, or if your fabric does fray easy using your pinking shears to stop the fraying.