Linguistically, medieval Mali was a wonderfully diverse place! The primary languages would have been in the Mande subfamily of the Niger-Congo, but the empire also had a sizable population of Fula (Fulani) speakers.

At least some people did speak Arabic. Of course we have the extensive manuscript collection of writings. And when Ibn Battuta visited Mali in the 14th century, he describes hearing the Quran sung in full during a meal, as well as prayers being said. He did use an interpreter most of the time, so we know Arabic wasn't the lingua franca.