Sartre’s involvement in the GP happened because the GP was banned - in common with a swathe of leftist groups post-68, including some Trots - resulting in over a 1,000 GPers being imprisoned on purely political grounds. Hence Defert’s involvement, as a GPer on the outside, in prison solidarity shit - with so many GPers inside, the GP understandably became oriented towards prison work. Initially it was around trying to get political status for their prisoners and have them segregated from the general population, but then they shifted to trying to radicalise the prison population and do things on behalf of all prisoners, which is when Foucault and Deleuze and the GIP happened. Defert says, btw, that Foucault chose the GIP acronym to signify the intercession of the intellectuals in the GP. OK, so Sartre was involved because the De Gaulle refused to allow him to be imprisoned under the rubric “one does not imprison Voltaire”, so by becoming titular editor of Cause de Peuple, Sartre gave some kind of cover to its, otherwise illegal, publication.