As usual, it does depend somewhat on when and where, but generally: Arabic. Once the invasion occurred, Muslims in Iberia were closely connected to the rest of the Muslim world by trade and politics, making Arabic the lingua franca there as elsewhere. Berber was also common, though, due to the strong presence of Berbers in both the initial invading force and subsequent waves of settlement. However, as the Reconquista gathered steam and more and more Muslims found themselves living under Christian rule, it became advantageous for those Muslims (called mudéjares) to have at least a working knowledge of Iberian Romance, i.e. Old Spanish--which was itself strongly influenced by Arabic. Nonetheless, Arabic remained common, especially for academic and administrative discourse (much as Latin in the Christian realm).