This paper presents an agent-based model of the labor market. It simulates the market in the recent period at the aggregate level and at the level of the principal categories of labor, on the basis of the decisions of heterogeneous agents, firms and individuals, who interact. These decisions rely on individual computations of profits and utilities, although rationality is bounded in such a complex environment. The theoretical structure that underlies the decisions is the search concept. We apply this framework to the case of France in 2011. The model is at a scale of 1/4700. It is fairly detailed on the institutions of the labor market that constrain the agents' decisions. Finally it is calibrated by a powerful algorithm to reproduce a large number of variables of interest. The calibrated model presents a consistent accounting system of the gross flows of the individuals between the main states, employment, distinguishing open ended contracts and fixed duration contracts, unemployment and inactivity. The simulation of the gross flows accounts enables us to analyze the patterns of mobility in a way that the observed statistics on gross flows, which are partial, cannot do. The model then characterizes the nature of the labor market under study, reproducing the high proportion of the fixed duration contracts in the hiring flows, and it points to a dualism of the French labor market.