This paper empirically investigates the asymptotic behaviour of the flood probability distribution and more precisely the possible occurrence of heavy tail distributions, generally predicted by multiplicative cascades. Since heavy tails considerably increase the frequency of extremes, they have many practical and societal consequences. A French database of 173 daily discharge time series is analyzed. These series correspond to various climatic and hydrological conditions, drainage areas ranging from 10 to 10(5) km(2), and are from 22 to 95 years long. The peaks-over-threshold method has been used with a set of semi-parametric estimators (Hill and Generalized Hill estimators), and parametric estimators (maximum likelihood and L-moments). We discuss the respective interest of the estimators and compare their respective estimates of the shape parameter of the probability distribution of the peaks. We emphasize the influence of the selected number of the highest observations that are used in the estimation procedure and in this respect the particular interest of the semi-parametric estimators. Nevertheless, the various estimators agree on the prevalence of heavy tails and we point out some links between their presence and hydrological and climatic conditions.