Virelai is one of the three formes fixes and is a type of formal poem from medieval France. It thrives on short lines, a focus on rhyme, and is written entirely in nonets (nine-line verses). Note that the song and poem forms are related but slightly different.
The rondel is a French verse form typically consisting of 13 octasyllabic lines and multiple refrains, though there are quite a few variants of the form. It is a descendant of the prolific rondeau, another older French form that also had an impressive amount of influence over formal poetry.
The quatern is a short quaternion (a poem divided into four parts) that employs a refrain that switches positions between each verse. The quatern is sixteen lines, cut up into quatrains that are each comprised of eight-syllable lines.
The bref double is a French quatorzain consisting of three quatrains and a couplet, which makes it not unlike an English sonnet. The main dividing points between the two are that the bref double features multiple unrhymed lines, a unique three-sound rhyme scheme, and a lack of meter.