The Vasconic substratum theory is a proposal that several western European languages contain remnants of an old language family of Vasconic languages, of which Basque is the only surviving member. The proposal was made by the German linguist Theo Vennemann, but has been rejected by other linguists.
According to Vennemann, Vasconic languages were once widespread on the European continent before they were mostly replaced by Indo-European languages. Relics of these languages include toponyms across Central and Western Europe.
Vennemann (2003) proposes that after the last Ice Age, Vasconic people (perhaps coming from Africa) resettled all of Western Europe. They gave names to the rivers and places. These names often persisted after the Vasconic languages were replaced by Indo-European languages in most of their area. The present Basque area in northern Spain and southern France is postulated to be a relic. This is based on parallelisms in Old European hydronymy that have been noted by Hans Krahe, and in culture by Marija Gimbutas, that are suggested to be relics of a pre-Indo-European substratum. Theo Vennemann believes that one of the substrata is Vasconic because typical elements of pre-Indo-European toponyms can be explained through the Basque language, for instance the element aran, Unified Basque haran "valley", in names like Val d'Aran, Arundel, or Arendal. However, most linguists believe that the probability of the hydronyms to have Indo-European origins is greater.
Another piece of evidence for the Vasconic language, according to Vennemann, is the persistence of vigesimal (base-20 counting) traits in Celtic, French, Georgian, the Resian dialect, and Danish. Vennemann regards the vigesimal system as a trait of the Vasconic language.