After the Three Mile Island accident in 1979 and the Chernobyl accident in 1986, the Fukushima accident shows that the probability of a core meltdown accident in an LWR (Light Water Reactor) has been largely underestimated. The consequences of such an accident are unacceptable except in the case of TMI2 (Three Mile Island 2) large areas around the damaged plants are contaminated for decades and populations have to be relocated for long periods. This article presents the French approach which consists in improving continuously the safety of the Nuclear Power Plants (NPP) on the basis of lessons learned from operating experience and from the progress in RandD (Research and Development). It details the key role played by IRSN (Institut de radioprotection et de sÛreté nucléaire), the French TSO (Technical and scientific Safety Organization), and shows how the Fukushima accident contributes to this approach in improving NPP robustness. It concludes on the necessity to keep on networking TSOs, to share knowledge as well as RandD resources, with the ultimate goal of enhancing and harmonizing nuclear safety worldwide. © 2012 Académie des sciences.