There are at least two sources that provide information on migratory flows in France. First are residence permits issued to adult immigrants of foreign nationality, which provide arrival dates and the duration of residence permits for legal immigrants. Second are annual population census surveys, which have taken place every year since 2004 and provide a snapshot of the population living in France at the beginning of the year. In particular they provide the arrival date in France of people born abroad. By restricting our analysis to a scope that is common to both sources, i.e. people of foreign nationality (excluding the European Economic Area and Switzerland), born abroad, and who came to metropolitan France aged 19 or over, the article proposes a model to reconcile data by estimating by Bayesian inference rates of presence in the annual census survey, and rates for obtaining residence permits according to the number of years spent in the country. After identifying from among the immigrants who have obtained a residence permit those who have been in France for at least a year, which is the condition for being included in the census, according to international definitions, estimates suggest that not all immigrants who entered the country in a year are present (or identified) in the census in their first year, and that from the third year onwards the proportion of those who are present for the census decreases on average by 3% per year (mainly due to those leaving the country). Seventy percent of these new immigrants obtained their residence permit during the year they arrived or the following year. There are major disparities between nationalities regarding their estimated inclusion in the census. Women seem to appear in the census more often than men, and the youngest people more than the oldest. Lastly, a detailed analysis of the two sources showed their respective strengths and weaknesses in estimating migratory flows.