Based on what? You can’t just say so because of geographic or racial reasons.

Based on linguistics. People have studied the grammar and vocabulary of languages all over the world and classified them into families based on common origins / evolution and characteristics. You can check it out here

https://en.wikipedia.org/wiki/Dravidian_languages - the family that most South Indian languages belong to.

https://en.wikipedia.org/wiki/Indo-Aryan_languages - the family that most North Indian languages belong to.

In addition, there are languages spoken in India that don't fit into these categories, and are part of other families :

https://en.wikipedia.org/wiki/Munda_languages - Part of the Austroasiatic language family.

https://en.wikipedia.org/wiki/Dzongkha - Part of the Sino-Tibetan family, spoken by a sparse population in West Bengal.

None of this classification is based on "geographic" or "racial" reasons. They're classified and studied as a science.

The truth is a lot more complex than these binary characterisations. All Indian languages have loanwords (tatsama, tadbhava). One interpretation is that Sanskrit is like bones of the linguistic body while other Prakrit languages provide it with muscle and mass. Sanskrit in it’s abstract form is very hard to use conversationally. Finally Hindi which is the dominant language in the north came from Hindustani which itself has heavy influence of Persian/Urdu.

Linguists have abounded these simplistic trees of ancestry a while back. Truth is all these languages interacted and improved one another. For example it’s likely that Dravidian languages were spoken in the Indus Valley civilization. That would make them the greatest ancestor. Sanskrit was formed much later and was likely influenced by it.

Indo Aryan itself is a racially rooted theory started by Europeans to extract familiar parts of Indian culture and define a collective identity. Reality is far more complex