Transport protocols that can exploit multiple paths, especially MPTCP, do not match the requirements of video streaming: high average transmission delay, too strict reliability, and frequent head-of-line phenomenons resulting in abrupt throughput drops. In this paper, we address this mismatch by introducing a cross-layer scheduler, which leverages information from both application and transport layers to re-order the transmission of data and prioritize the most significant parts of the video. Our objective is to maximize the amount of video data that is received in time at the client. We show that current technologies enable the implementation of this cross-layer scheduler without much overhead. We then demonstrate the validity of our approach by studying the performance of an optimal cross-layer scheduler. The gap between the performance of the traditional scheduler versus the optimal scheduler justifies our motivation to implement a cross-layer scheduler in practice. We propose one implementation with basic cross-layer awareness. To evaluate the performance of our proposal, we aggregate a dataset of real MPTCP sessions and we use video stream encoded with HEVC. Our results show that our cross-layer proposal outperforms the traditional scheduler. Viewers not only benefit from the inherent advantages of using MPTCP (such as a better resilience to path failure) but also get a better QoE compared to the traditional scheduler.