This might provide a bit of inspiration even though it isn't specifically for a French braid. It does have lots of horizontal bars much like the braid:
Start at the 9:43 mark or so for the quilting part
https://www.youtube.com/watch?v=v39RAlkaLTo
also, a bit more inspiration for you here on youtube...maybe?
This too is Angela Walters- the Midnight Quilt Show. look at the log cabin video or the chevron, maybe?
https://www.youtube.com/results?sear...outube+channel
more ideas here on youtube for strip type quilts
https://www.youtube.com/results?sear...r+strip+quilts
here are some designs for borders that might work for your braid...pick one design for all the braid strips or mix several designs throughout?
https://duckduckgo.com/?q=quilting+i...=v314-1&ia=web
more border design ideas on pinterest:
https://duckduckgo.com/?q=free+print...ages&ia=images
this one looks like stitch in the ditch
https://i.pinimg.com/originals/a5/4b...8a7175d87c.jpg
here is edge to edge from pinterest like lindaschipper suggeste....looks great
https://i.pinimg.com/originals/db/40...6653b86f14.jpg
or maybe just echo your seams?
sorry....got a bit carried away