According to Buddhist tradition he spoke Pali, a Pakrit from northern India in which most early Buddhist scripture first appears, before the rise of Buddhist Hybrid Sanskrit as the liturgical language.

This is despite the Buddha's own urging of priests to teach in the local vernacular (sakayā niruttiyā), instead Pali was preserved as a language of faith throughout much of the Buddhist world, particularly among Theravada Buddhism.

In reality, the Buddha was almost certainly multilingual, as a member of the Kshatriya caste he would most likely have been literate in Sanskrit, which was a language of prestige and learning, related to and sharing many features with the Pakrits or "vernacular" languages.

Most of my information comes from Empires of the Word: A Language History of the World, by Nicholas Ostler. It's a very interesting book, although as it is an attempt to overview language spread and change across the world over a very long timeframe it does probably gloss over some details.