Fall detection in specialized homes for the elderly is challenging. Vision-based fall detection solutions have a significant advantage over sensor-based ones as they do not instrument the resident who can suffer from mental diseases. This work is part of a project intended to deploy fall detection solutions in nursing homes. The proposed solution, based on Deep Learning, is built on a Convolutional Neural Network (CNN) trained to maximize a sensitivity-based metric. This work presents the requirements from the medical side and how it impacts the tuning of a CNN. Results highlight the importance of the temporal aspect of a fall. Therefore, a custom metric adapted to this use case and an implementation of a decision-making process are proposed in order to best meet the medical teams requirements. Clinical relevance This work presents a fall detection solution enabled to detect 86.2% of falls while producing only 11.6% of false alarms in average on the considered databases.