SummaryREM sleep behaviour disorder (RBD) is common in narcolepsy type 1 (NT1). Abnormalities in the reward system have been observed in NT1, possibly related to impaired orexin projections towards the mesolimbic reward system, but also in RBD when associated with Parkinson's disease. Our study aimed to explore the psychobehavioural profile of NT1 patients with and without RBD compared with healthy controls (HC). Forty patients with NT1 were compared with 20 sex‐ and age‐matched HC. All patients with NT1 underwent a video‐polysomnography including a measure of REM sleep without atonia (RSWA). The following neuropsychobehavioural variables were assessed: apathy, impulsivity, depression, cognition, subjective and objective attention, sensation‐seeking, and behavioural addictions. The patient population included 22 patients with NT1‐RBD and 18 patients with NT1‐noRBD. Compared with the healthy controls, patients with NT1 had higher scores of apathy, impulsivity, and depression; a lower score on global cognition, and poorer self‐perceived attention. No differences were found between patients with NT1 with and without RBD in all neuropsychological variables, except for impaired objective attention in patients with NT1‐RBD. In patients with NT1, a positive correlation was observed between RSWA and both apathy and impulsivity subscale. Moreover, in patients with NT1‐RBD, RSWA was positively correlated with depression. Patients with NT1 showed higher depression, apathy, and impulsivity compared with controls. These measures correlate with the severity of RSWA, suggesting a transdiagnostic association between RBD and abnormalities of the reward system at least for patients with NT1.