The Brahmanists have always regarded Sanskrit, as the Mother of Languages. As a matter of fact, this will be echoed in many of the Hindu bunch from Modern India. Latest to join in the Bandwagon, is the Tamil Dravidian nationalists, who claim Tamil to be the progenitor of all langagues. Even Though, no Indian Language or for that matter any other language, can truly claim as being the original Proto-Language of the World.
The existence of such a hypothetical Proto-World Language is itself contested. I prefer to view as Languages originally emerging as independant from each other, later influencing each other as different cultures spread around the cloud.
It is not surprising for the Brahmanists to claim the Vedic language as the Mother of All Languages. For according to Vaidikas, Vedas are Apauruṣeya (Not [authored] by Men). It was heard by the Rishis, who were just instruments for writing the cosmic sound that they heard. Vedas are also considered as Anādi (Without Begninning). So for the everlasting and supreme Vedas to be supramundane, the language in which it is composed of is also deemed to be supramundane and perfect. It was language of the gods.
Now, coming to the Shramanic religions namely Buddhism and Jainism. They started out with the vernacular prakrita languages. They were more inclined to use the language of the masses to spread their teachings. In fact, many of the initial literature in the Indian regional language were produced by the Shramanas. At one instance, the Buddha is said to have explicitly forbidden his teachings to be Versified in Vedic Language (Chandas), but to be taught in the language of the masses. But as irony befalls, the Shramanas themselves fell into the same trap as their Vedic counterparts. They began considering their own version of liturgical Prakrit as the original source language !