The sacred liturgical language of ancient India in which the Vedas were composed is Sanskrit.
More precisely, the Vedas were composed in Vedic Sanskrit, the oldest recorded form of the Sanskrit language. The Rigveda, generally considered the earliest Veda, was composed orally during the second millennium BCE. The other three Vedas are the Yajurveda, Samaveda, and Atharvaveda.
The Vedas were preserved through highly disciplined oral recitation for centuries before being written down. Priests used elaborate memorization techniques to protect the exact sounds, accents, and sequence of the hymns, because correct pronunciation was considered essential in ritual practice. This is why Sanskrit remained central to Hindu ceremonies even after it ceased to be an everyday spoken language.
A common mix-up is confusing Sanskrit with Avestan, another ancient Indo-Iranian language associated with Zoroastrian scriptures. Pali is associated especially with the Buddhist canon, while Tamil is an ancient Dravidian language with its own major literary and religious traditions. Classical Sanskrit was later standardized by the grammarian Pāṇini, whose work helped distinguish it from earlier Vedic Sanskrit.