Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain the network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable generation expansion planning problem, called R-ETEM, in which demand responses of EV users are uncertain. Then, we employ a linear quadratic game to simulate the average charging behavior of the EV users. The two models are coupled through a dynamic price signal broadcasted by the utility. Mean field game theory is used to solve the linear quadratic game model. Finally, we develop a new coupling algorithm between R-ETEM and the linear quadratic game with the purpose of adjusting in R-ETEM the uncertainty level of EV demand responses. The performance of our approach is evaluated on a realistic case study that represents the energy system of the Swiss "Arc Lémanique" region. Results show that a robust behaviorally-consistent generation expansion plan can potentially reduce the total actual cost of the system by 6.2% compared to a behaviorally-inconsistent expansion plan.