Census undercounts of young children, especially those aged under 5, persist worldwide. In the French census, an average of 1 in 20 young children have been missing from enumeration since annual census surveys were introduced in 2004. This study uses linked census data from the INSEE Permanent Demographic Sample to identify which children are omitted and from where, and offers possible explanations for why they are missing. The analysis finds that the specific omission of young children accounts for two-thirds of omissions; that the omission of young children is associated with their characteristics, especially those residing in complex households; and that internet enumeration has a positive impact on the enumeration of young children, reinforced by the recent redesign of the census household questionnaire.