While the most famous writer about this period is Grégoire de Tours, who a century later, wrote 'Historia Francorum', Grégoire is subjective about history as he tried to please the new masters of the Gauls.
Note that the Gaulish language seems to have gone extinct around this time, so talking about "5th Century Gauls" may be a bit of an anachronism. Gallo-Roman might be better?– T.E.D. ♦Jan 23, 2017 at 22:37
I think that the main contemporary sources for Western Europe are de Chronica Gallica of 452, Chronica Gallica of 511, and the Chronicle of the bishop Hydatius.
The first two were written in southern Gaul, and end in 452 and 511.
The Chronicle of Hydatius was written in Galicia by Hydatius, a local bishop, circa 468. While initially intended to be an universal continuation of the annals by St. Jerome, it slowly turns into the narration of the decomposition of the Empire in Western Hispania in general and Galicia in particular: the settlement of the Germanic Suebes and Vandals, the flight of Vandals into Africa, and the subsequent conflicts and wars of Suebes, Visigoths, Romans, and the partially romanized locals.
Also, the very influential "Historiae Adversus Paganos", by Orosius were written circa 418.
Only one source written at that time exists as of today: the letters written by 'Sidoine Apollinaire' (or 'Caius Sollius Apollinaris Sidonius' in Latin). He was Prefect of Rome and a clerk of the Roman administration in the first part of his life. He witnessed the end of the Roman Empire in Gaul and then was appointed as first Christian Bishop of the city of Clermont. As such he managed to negotiate a relatively smooth transition from Roman command to Visigoth command over the city and its surroundings. From then on, the Roman empire was history in most of Gaul. A new era began, known broadly as the Middle Ages. His texts (letters and poetry) are those of a watcher and the only sources of this century in Gaul.