Climate change is defined often as the long-term fluctuations in climate patterns affecting the planet globally. Its main observed consequences are a rise in average temperatures in many parts of the globe, and an increase in the frequency and severity of extreme weather events, such as floods, droughts, or wind storms. Climate change is also associated with a rise in sea levels, more frequent and more severe wildfires, a loss of biodiversity, as well as other disrupting events that can have a serious economic impact. These new climate risks are increasingly affecting the frequency and the severity of claims in different insurance branches. In order to help insurance companies predict and manage climate risks, North-American actuaries have defined the Actuaries Climate Index™ (ACI), that combines information from several important weather variables in the historical records of United States and Canada. The ACI shows a significantly increasing trend over recent years. Now that the ACI provides a factual and objective climate risk measure for North-America, the need arises to test if a similar tool can measure the impact of climate change in other parts of the planet, and if the change is similar or not. Despite the observed global nature of climate change, different regions and countries can be affected in different ways. As a first step it is important to check if the ACI methodology is useful to assess climate risk even outside the United States and Canada. This paper proposes the use of the same ACI methodology to calculate an actuarial climate index with the climate data of France, which we call the French Actuarial Climate Index (FACI). The paper reviews the methodology and the data used to obtain the FACI, and with it studies the impact of climate change in France, including high-resolution analyses, per component, season and region. Together with the recent indices calculated for Spain and Portugal, this FACI represents one more step towards the definition of a European index.