A FANET is a type of very low density ad hoc network where all its nodes move irregularly and quickly. In addition to the environmental variables, several characteristics influence the performance of FANETs, such as speed, mobility, and drone density. In order to solve the problem of energy consumption and data loss for FANETs, we propose a stable and energy-efficient multipath routing protocol based on the cuckoo search algorithm named SE-RPCS. A fitness function is integrated to choose the best path among all the new paths generated after the end of the cuckoo search algorithm. This fitness function relies on two constraints: energy and link stability. The performance of our protocol is compared to AOMDV and AODV protocols. The results show that SE-RPCS improves network performance, provides more efficiency and reliability.