Short history of the texts
First there was one Psalm by Marot in the vernacular, the penitential Psalm 6, probably ca. 1530, getting a wider circulation in an appendix to Marguerite d'alençon's Miroir de l'âme pecheresse. In manuscript they circulated and grew to the first official edition of 30 Psalms in 1541/2, to which Marot added 20 new Psalms (19 Psalms and the Canticle of Simeon) in 1543. Almost from the start, and even pre-dating them (ca. 1533), the French Psalters also contained some extra texts: liturgical or for personal devotion. Once more it was Clément Marot who wrote them (or under whose name they were published). The seond page from this article sketches the origin.
The two pages tell the story of their origin. It's a short summary of chapter two from my dissertation: Clément Marot and Religion, (Brill, 2010), with some updates based on new bibliographic discoveries. If interested in more you are invited to visit my Clement Marot website.