The possibilities that emerge from micro-blogging generated content for crisis-related situations make automatic crisis management using natural language processing techniques a hot research topic. Our aim here is to contribute to this line of research focusing for the first time on French tweets related to ecological crises in order to support the French Civil Security and Crisis Management Department to provide immediate feedback on the expectations of the populations involved in the crisis. We propose a new dataset manually annotated according to three dimensions: relatedness, urgency and intentions to act. We then experiment with binary classification (useful vs. non useful), three-class (non useful vs. urgent vs. non urgent) and multiclass classification (i.e., intention to act categories) relying on traditional feature-based machine learning using both state of the art and new features. We also explore several deep learning models trained with pre-trained word embeddings as well as contextual embeddings. We then investigate three transfer learning strategies to adapt these models to the crisis domain. We finally experiment with multi-input architectures by incorporating different metadata extra-features to the network. Our deep models, evaluated in random sampling, out-of-event and out-of-type configurations, show very good performances outperforming several competitive baselines. Our results define the first contribution to the field of crisis management in French social media.