Evolution and accessibility of smart-phones have led to a huge demand in network bandwidth. The ubiquitous use of smart-phones in high-speed trains poses a unique challenge in delivering high-speed internet service on board. This challenge can be overcome by employing free-space optics, an alternative to radio-frequency technology. Previous coverage models for ground-train communications employed single laser systems with a larger divergence angle to cover a larger distance. Larger divergence angles lead to larger geometric losses, which may result in a non-reliable communication link. This study proposes a sectorised multi-beam coverage model with a smaller divergence angle to reduce the impact of geometric losses in the system. This study also proposes two receiver (Rx) architectures for Rxs deployed on the train. Along with geometric losses, the atmospheric attenuation is taken into consideration for the FSO link. The performance of the ground-train communications system in terms of bit-error-rate is evaluated under weak turbulence conditions via numerical simulation.