To address the satellite access problem in geostationary earth orbit and low earth orbit (GEO-LEO) heterogeneous satellite networks characterized by periodic satellite motion and time varying user demands, this study develops a grey clustering enhanced proximal policy optimization (GC-PPO) method with invalid action masking. First, a GEO-LEO heterogeneous satellite networks is established and key state attributes are modeled based on satellite networks (SNs) characteristics. A grey clustering model is introduced to generate grey clustering coefficients reflecting heterogeneous satellite conditions and user preferences. These coefficients are used as unified observations for the reinforcement learning agent and are further incorporated into action masking to eliminate infeasible decisions. The integration of grey clustering model with proximal policy optimization improves decision efficiency, and neural network approximation in DRL enables implicit weighting of grey clustering coefficients, providing an adaptive mechanism for handling similarities among satellite state representations. Simulation results demonstrate that the proposed strategy reduces blocking and handover rates while improving quality of service (QoS).