An online forum asked about an ancient text named the Acts of St. Saturninus. I had not heard of these, and my investigation is perhaps worth writing up.
The Passio S. Saturnini is a text which describes the death of Saturninus and other martyrs of Toulouse in Gaul during the Decian persecution. It belongs to that category of martyrdoms which Ruinart labelled “sincera”, i.e. authentic rather than merely a later invention.. The text is numbered BHL 7495-6. (Note that a later, 7-8th century text is much longer and numbered BHL 7491, and was edited in 2002 and published by Herder).
In its current state, the Passio S. Saturnini is a late text, edited in the second decade of the 5th century (certainly before 450 AD), two centuries after the death of the bishop, at the moment when his cult began, thanks to the translation of his relics from the modest tomb where he had been buried into a new basilica. The author of it is very definitely a clergyman of Toulouse living at the time of bishop Exuperius, or soon afterwards.
Cabau wrote notes on the bishops of Toulouse in this period, which may be found here.
Patrice Cabau, “Opusculum de passione ac translatione sancti Saturnini, episcopi Tolosanae ciuitatis et martyris. Édition et traduction provisoires”, in: Mémoires de la Société archéologique du Midi de la France 61, 2001, p. 59-77. This includes a full bibliography. Online here.
Pierre Maraval, Actes et Passions des martyrs chrétiens des premiers siècles. Introduction, traduction et notes, in: Sagesses Chrétiennes, Cerf, 2010, pp. 181-192. Online here.
I have found no sign of a translation into English, unfortunately.