This paper introduces a framework for cross-layer management of data transmissions in free-space optical (FSO) systems over atmospheric turbulence channels, in which link layer automatic repeat request (ARQ) and physical layer adaptive modulation and coding (AMC) are integrated to improve the system's spectral efficiency. The system performance is analytically studied in terms of average frame-error rate and average spectral efficiency, for which we derive closed-form expressions. In numerical results, we show how the proposed scheme outperforms a conventional one, and discuss cross-layer designs for parameters' selection in both physical and link layers to optimise the system performance over different atmospheric turbulence conditions.