In this paper, we focus on the problem of robust rolling-stock planning for French passenger trains. First, we characterize robustness and define some indicators for the evaluation of rolling-stock rosters. We take a particular interest in homogenizing turning-times in a roster in order to absorb potential delays. Then, we propose a new approach to solve the problem of robust rolling-stock planning. The SNCF reference tool (PRESTO) calculates a solution to the rolling-stock planning problem. It consists of a multi-step approach to cover demand while minimizing operating costs, and to further add maintenance slots to the roster. We propose an integrated ILP model to add robustness to a roster while maintaining low operating costs compared to PRESTO. We have carried out tests on nine real French regional transport instances, and we use a simulation module to evaluate the results. We observe a significant improvement in robustness indicators while maintaining low operating costs and meeting maintenance requirements.