This is a question I could never really find a good answer to. In general, would its founders have been speaking a Mande language still in use today?
The short answer is āMandingā.
Linguists would refer to this as āProto-Mandingā because itās something that we have no documented evidence of, so its forms in terms of grammar and vocabulary are based on theorized reconstructions of the major living Manding varieties that we know today: Bambara, Jula, Maninka and Mandinka, etc.
The name āMandingā is slighly misleading because the name of the language itself in the language itself as the time was almost certainly: mandenkakan (< manden-ka-kan ālanguage of the people of Mandenā). This is the name from which the modern varieties such as āManinkaā (that is, āManin-ka-kanā) and āMandinkaā (that is, āMandin-ka-kanā) descend.
The so-called āMali Empireā was, of course, a political formation that emerged from a region that in the language is called āMandenā.