The French word gave, as used in the western part of the Pyrenees, is a generic name referring to a torrential river. In the central part of the mountain range, the term for this is neste.
The word gave derives from the old Gascon gabar, attested as gabarrus in medieval Latin.[1] Based on a pre-Celtic root *gab meaning 'hollow' (thus 'throat'), it refers to lower places, valleys and rivers. It is widely found in placenames of Gascony as Gabardan, Gavarret, Gavarnie, Gabas, etc. The name of the Gabali (the ancient people living in Gévaudan) is supposed to be related to this stem.
The final -r is missing because it was lost in Gascon: gabar > gabà > pronounced as /[ɡabɵ]/.