I recently made a quilt suggested by a Fons and Porter show. All of the pieces were half hexagons. With everything precut at precisely the correct angle, the braids went together super easily. I have made other braids, including French braids, but none I liked any better.
I you really want a French braid from your layer cake, remember that you will need right and left handed pieces, so pair your fabrics face to face to get both shapes, cut the strips, then sub-cut at the center on a 45*. Be sure to make a pile of each type of piece to avoid frustrating searches. It works well to use only one or 2 colors for your row of squares.