Shortages of drugs and medical devices have tended to increase in France and worldwide, with consequences for patients and healthcare professionals. Preventing shortages of health products has become a priority for regulatory authorities, including the French National Agency for Medicines and Health Products Safety (ANSM). To highlight perspectives for a better prevention, we described and analyzed the management of shortages in the availability of health products in France over the last 10 years. The supply chain was mapped to identify the main causes of shortages and stakeholders involved in managing shortages throughout the supply chain. National and European initiatives and regulatory measures were reviewed. A retrospective nationwide data analysis from the French reporting system of health product shortage reports was conducted over 10 years for drugs (2013–2022) and over an 18-month period for medical devices, from 1st March 2022 to 31st August 2023. An increase in drug shortage reports was observed, rising from 404 in 2013 to 3,761 in 2022 for drugs, with a relatively constant distribution of affected therapeutic classes. In 2022, the main reported causes of drug shortage risk were insufficient production capacity (27.1%), increased sales volume (21.5%), or lack of supply (13.6%). Over half of the reports on medical devices (55.4%) were objectified as indispensable, and their causes were mainly due to a lack of supply (48.2%), discontinuation of marketing (14.9%), increased sales volume (13.2%), and regulatory reasons (9.6%). ANSM and French authorities have engaged a public health policy for prevention and management of health product shortages including financial penalties, minimum safety stocks for Major Therapeutic Interest drugs, and a shortage management plan. Based on 10 years of experience, four priority measures have been identified to anticipate the risk of heath products shortages based: the importance of a national coordination from raw materials to local market, the implementation of new prevention and management actions in the supply chain, strengthening European cooperation and regulation including the establishment of a list of critical drugs, and promoting transparency and information.