Introduction Studies have shown that depression or anxiety occur in 10–20% of pregnant women. These disorders are often undertreated and may affect mothers and children’s health. This study investigates the relation between antenatal maternal depression, anxiety and children’s early cognitive development among 1380 two-year-old children and 1227 three-year-old children. Methods In the French EDEN Mother-Child Cohort Study, language ability was assessed with the Communicative Development Inventory at 2 years of age and overall development with the Ages and Stages Questionnaire at 3 years of age. Multiple regressions and structural equation modeling were used to examine links between depression, anxiety during pregnancy and child cognitive development. Results We found strong significant associations between maternal antenatal anxiety and poorer children’s cognitive development at 2 and 3 years. Antenatal maternal depression was not associated with child development, except when antenatal maternal anxiety was also present. Both postnatal maternal depression and parental stimulation appeared to play mediating roles in the relation between antenatal maternal anxiety and children’s cognitive development. At 3 years, parental stimulation mediated 13.2% of the effect of antenatal maternal anxiety while postnatal maternal depression mediated 26.5%. Discussion The partial nature of these effects suggests that other mediators may play a role. Implications for theory and research on child development are discussed.