Etymology

From Old French Gascoigne, from Gasconia, from Wasconia, from Vasconia from Latin Vascones, plural of Vasco, from Ancient Greek ουασκωνους ‎(ouaskōnous), as used by Strabo in his Geographica (23 CE), Book III.^[1] either from αἴξ ‎(aíx, “goat”) (literally “he-goat people”), or variant of Ausci (from which Aquitan, Occitan, and perhaps related to Euskara). Cognate to Basque (compare to Gascon).

For sound changes: /v/ → /w/ occurred in the change from Latin to Proto-Romance, while /w/ → /g/ common in (non-Iberian) Romance languages, notably French; compare warranty and guarantee, William and Guillaume. By contrast, /v/ developed into /b/ and /β̞/ in Spanish and Gascon, under influence of Basque, hence the divergence.