We theoretically analyze the performance of free-space optical (FSO) systems using cooperative-ARQ (C-ARQ), a joint scheme of automatic-repeat-request (ARQ) and cooperative diversity, over atmospheric turbulence channels. We also propose a modified C-ARQ (M-C-ARQ) scheme that allows relay nodes to store a copy of frames for the more efficient response to transmission failure so that both transmission delay and energy consumption can be improved. Using Markov chain-based analytical models for both schemes, the system performance is analytically studied in terms of frame-error rate, goodput and energy efficiency, which directly reflect the transmission delay and energy consumption. Numerical results confirm that the proposed schemes outperform conventional ones. In addition, we discuss cross-layer design strategies for selecting parameters in both physical and link layers in order to optimize the performance of FSO systems over different atmospheric turbulence conditions and channel distances.