Are you familiar with Bart Halpern fabrics? If not, just take a quick peek at the website. This company pleats fine fabrics onto a tricot knit backing in a dozen or more different patterns.
I was lucky enough to be asked to make shades out of a sheer linen pleated into the "wide wave" pattern.
My biggest concern was to not shrink the linen fabric while applying the trim. I carefully tabled the fabric, aligning the "waves" with the table grid, and hand-sewed the side hems.
I planned the trim layout, pinned it to size into the U-shape, and machine-sewed the mitered corners. The corner seam was clipped and pressed open. I used Bortenfix adhesive tape from Dofix to apply the trim- after first having tested the fabric to be sure it wouldn't distort.
In this case there were several reasons for hand-sewing.
First, I knew I was going to be applying steam when it came time to fuse the trim to the face, so I wanted to keep the steam to a minimum.
Secondly, I wanted the fabric to lay naturally, and sometimes an adhesive will secure the grainline in an awkward way- especially with a delicate, grainy sheer.
Most importantly, I wanted the hem to not be wider than the inner edge of the trim, and I wanted the rings to not be sewn through the trim, so, therefore, because the rings would have to be placed past the hemline, I wouldn't have those ring stitches to provide backup security for the hemline. Which is why I hand-sewed the side hems. Whew, I hope you followed that!