Departure time choice models have a crucial role in transportation network planning in order to provide planners with predictions about the optimal traffic load. This paper introduces a new dynamic departure time choice framework based on the so-called Mean-field Games (MFGs) theory proposed by Lasry and Lions. MFGs models aim to analyze large population differential games. This feature gives us a unique opportunity to design a departure time choice equilibrium model in a scale-free transportation system. The proposed framework is the combination of two components: (i) the reaction of travelers to the traffic congestion by choosing their departure time to optimize the travel cost; (ii) the aggregation of the actions of the travelers, which determines the congestion level of the system. The first component corresponds to a classical game theory model, while the second one captures the interactions of the travelers at the macroscopic level. We use the generalized bathtub model recently proposed by Jin to represent the traffic dynamics at the network level. First, we provide a continuous model to investigate the equilibria and then give a discrete approximation of the system from deterministic differential games models. Finally, we show on a real test case that the model can represent the departure time choice equilibrium for multiple preferred travel time with heterogeneous trip lengths wile the framework is capable of considering a large number of players.