The methodology used in wind resource assessments often relies on modeling the wind-speed statistics using a Weibull distribution. In spite of its common use, this distribution has been shown to not always accurately model real wind-speed distributions. Very few studies have examined the arising errors in power outputs, using either observed power productions or theoretical power curves. This article focuses on France, using surface wind measurements at 89 locations covering all regions of the country. It investigates how statistical modeling using a Weibull distribution impacts the prediction of the wind energy content and of the power output in the context of an annual energy production assessment. For this purpose it uses a plausible power curve adapted to each location. Three common methods for fitting the Weibull distribution are tested (maximum likelihood, first and third moments, and the Wind Atlas Analysis and Application Program (WAsP) method). The first two methods generate large errors in the production (mean absolute error around 5 %), especially in the southern areas where the goodness of fit of the Weibull distribution is poorer. The production is mainly overestimated except at some locations with bimodal wind distributions. With the third method, the errors are much lower at most locations (mean absolute error around 2 %). Another distribution, a mixed Rayleigh–Rice distribution, is also tested and shows better skill at assessing the wind energy yield.