When a fast kinetic natural disaster occurs, it is crucial that crisis managers quickly understand the extent of the situation, especially through the development of "big picture" maps. For many years, great efforts have been made to use social networks to help build this situational awareness. While there are many models for automatically extracting information from posts, the difficulty remains in detecting and geolocating this information on the fly so that it can be placed on maps. Whilst most of the work carried out to date on this subject has been based on data in English, we tackle the problem of detecting and geolocating natural disasters from French messages posted on the Twitter platform (now renamed "X"). To this end, we first build an appropriate dataset comprised of documents from the French Wikipedia corpus, the dataset from the CAp 2017 challenge, and a homemade annotated Twitter dataset extracted during French natural disasters. We then developed an Entity-Linking pipeline in adequacy with our end-application use case: real-time prediction and peak resiliency. We show that despite these two additional constraints, our system's performances are on par with state-of-the-art systems. Moreover, the entities geolocated by our model show a strong coherence with the spatiotemporal signature of the natural disasters considered, which suggests that it could usefully contribute to automatic social network analysis for crisis managers.