To achieve real-time transmission of extensive remote sensing data, the combination of space-air-ground integrated networks (SAGINs) and free-space optical (FSO) technology is considered a suitable solution. However, the strongly attenuated atmosphere environment that covers long spatial distances and frequent handover of user-to-data links seriously affect the reliability of FSO links. As a relay linking the satellite layer and the ground layer, the introduction of high altitude platform (HAP) shortens the ultra-long satellite-to-ground FSO links, largely mitigating unreliable tropospheric connections. In order to achieve the improvement of the reliability of the whole SAGIN system, this paper integrates the space, air and ground three-layer network through HAP networking (HAPN). Based on HAPN architecture, the reliability enhancement scheme for two-hop FSO links is further designed. The first step is to reduce the attenuation of atmosphere turbulence by adjusting the HAP zenith angle through distanced clustering and Tabo search algorithms. The second step is to reduce the link handover times by extending the time window flexibly through HAP networking. The results show that the proposed schemes based on HAPN improve the reliability of the whole process of data transmission.