A French curve is used to draw curves at the armhole, neckline, curved darts, sleeve cap curves, and hipline curve, etc. They are transparent and some come with a straight edge including a Seam Allowance Guide and Grading Rules.
French curves come in a variety of sizes and shapes.
In this first image a French Curve is used to make the curve at the armhole of the Bodice Block:
The French Curve is used to join points A, B & C. Note that you may have to move the Curve and blend the lines.
Click on any of the images to view a larger version. It will open in a new window.
For the Sleeve Block, the French Curve is used to make each one of the four curves.
The two back curves of the sleeve are shown, for the front you do the same reflected on the other side.
Some French Curves have a seam allowance guide which makes makes adding a seam allowance on straight lines easier.