A backcalculation approach allows a reconstruction of the history of hepatitis C virus (HCV) infection in France and predictions of mortality from hepatocellular carcinoma (HCC) related to the virus. The model uses information from the literature about the natural history of the disease, epidemiological data about infected subjects in three French cohorts, and mortality data from national statistics. It seeks to determine the annual transition probabilities from chronic hepatitis to cirrhosis and the HCV incidence per year in the past. These unknowns are found by fitting the observed deaths from HCC that are attributable to HCV. Optimal values for these unknowns then allow to project the number of HCC deaths attributable to HCV for each year through 2025 (for patients infected before 1996). The model traces the HCV epidemic in France back to around the 1940s. It predicts that HCC mortality related to HCV will continue to increase through 2020 in the absence of treatment, with a 150% increase in the yearly incidence among men and 200% among women. The model also confirms that progression to cirrhosis depends strongly on sex and age. At any age, the annual probability of progression is 10 times greater for men than for women. Moreover, for men aged between 61 and 70 years, this probability is 300 times greater than that for men aged between 21 and 40 years.