Adopting full frequency reuse in High Throughput Satellite (HTS) systems is expected to cope with huge communication demands and large user populations. Moreover, a kind of multicast transmission, which embeds the data of several users in each frame, can be employed to increase the efficiency of HTS systems. Multicast precoding is usually utilized in such systems to mitigate the co-frequency interference between beams and improve the efficiency of transmission. In this context, considering that the number of users may exceed the number of available communication resources in the system, we investigate user scheduling for the multicast transmission in HTS systems with full frequency reuse and multicast precoding. We perform user scheduling according to the user channel state information and decouple the scheduling problem into two phases: intra-beam and inter-beam scheduling. Intra-beam scheduling determines the users involved in the transmission of each frame with the purpose of reducing the influence of the multicast fashion. For intra-beam scheduling, we put forth a fixed-size user grouping algorithm. In contrast to previous studies, this algorithm takes the interference among beams into consideration during the scheduling. In inter-beam scheduling, user groups belonging to different beams are scheduled to improve the performance of the multiplexed transmission. An inter-beam scheduling algorithm is proposed to improve the fairness among users. The simulation results verify the superiority of the proposed algorithms in terms of fairness and spectral efficiency.