The operational ALADIN-France 3D-Var system is based on static background error covariances calculated off-line during a few week past period. In this study, the impact of an online updated specification of background error covariances is evaluated in the ALADIN-France system. This evaluation is done by comparing three experiments, respectively based on (i) covariances calculated from a monthly average over a past period, (ii) covariances calculated from a monthly average over the period of study, and (iii) covariances calculated from a sliding daily average over the period of study. First, it is shown through a comparison between experiments (i) and (ii) that updating the monthly average of error covariances has a positive impact on the short-range forecast quality. This is related to the specification of covariances which are more representative of average weather regimes at play during the period of study. Second, a comparison between experiments (ii) and (iii) indicates that additional positive impacts of a daily update of error covariances are also visible, although they tend to be somewhat localized and modest during this period. These impacts are illustrated by case studies for humidity during an anticyclonic situation, and for wind during a cyclonic event. These results support the idea to consider an online updated specification of background error covariances.