The impact of aviation on climate change due to CO2 emissions is well established and is associated with much less uncertainty than the non CO2 effects. Among the non CO2 effects contrails formation and their evolution into cirrus-type clouds remain a subject of considerable uncertainty. A frequently overlooked source of uncertainty arises from the sensitivity of climate models to adjustable parameters used to represent the effect of subgrid-scale processes. The limited number of state-of-the-art climate models with an explicit contrail representation makes it challenging to evaluate model sensitivity of contrail radiative forcing to parameters and backgroud atmospheric conditions. To better characterize the contrail radiative forcing and its evolution it is therefore necessary to develop their representation within a large range of existing climate models. Here we develop and evaluate a new parameterization of contrail cirrus for the ARPEGE-Climat atmospheric model. The representation of the ice-supersaturated regions, where contrails persist, agrees well with in-situ and satellite observations, as well as the simulated contrail microphysical properties. With this parameterization, and using the ERA5 reanalysis to nudge the ARPEGE-Climat model, we estimate that for the air traffic of the year 2019 the global mean annual contrail coverage is 1.27%. In addition, the global mean annual instantaneous radiative forcing is estimated to be 66.2 mW/m2, although this result is sensitive to the choice of some key parameters of the contrail-cirrus parameterization. These findings are consistent with similar published results obtained using the same flight inventory but based on different methods of representing contrail effects.