Gibbon's main source in Chapter XXXVIII is Gregory of Tours (c. 538 - 594). He was the son of a senator from Clermont (Sidonius Apollinaris' see) who seems to have died while Gregory was still quite young. Gregory was educated by his uncle Avitus, the bishop of Clermont. In 573 Gregory became bishop of Tours. Many of his predecessors were his relatives. He is best known for his "Ten Books of Histories" or as it is more commonly known these days "The History of the Franks."
Some pictures of artefacts from Gregory's time.
Gaul after the death of Clovis (from wikipedia)
Articles on Gregory:
wikipedia (usual caveats apply)
La France pittoresque (includes a picture of a 1939 French stamp issued to commemorate the 1400th anniversary of Gregory's birth)
History of the Franks
Complete Latin text
Excerpts in English translated by Brehaut
Penguin Classics has an English translation, but apparently the introduction is not too well thought of.
English translation of excerpts.