Purpose This study aims to investigate the relationship between a positive leadership style [i.e. authentic leadership (AL)] and nurses’ psychological health (i.e. nurses’ flourishing and satisfaction with work–family balance), including psychological capital (PsyCap) as a mediational variable. Design/methodology/approach A cross-sectional study was conducted with a self-report questionnaire including 1,076 nurses from public and private hospitals in France. Findings Structural equation modeling results revealed that AL is related to nurses’ flourishing and satisfaction with work–family balance and that PsyCap acted as a partial mediator between this leadership style and positive outcomes. Practical implications This research indicated that hospitals can enhance nurses’ psychological health not only in their work but also in their lives in general by improving leaders’ authentic management style and developing PsyCap (e.g. staffing, training and development). Originality/value An original feature of this paper concerns its focus on the mediating role of PsyCap in the relationship between AL and these positive outcomes. Moreover, this study underlined the influence of leadership style on nurses’ psychological health beyond occupational health. The research makes a valuable contribution to the existing AL literature by establishing a new explanatory model of AL and nurses’ psychological health in the French context. It also highlights the interest in developing this leadership style in health-care settings.