The cognate advantage in bilingual children varies in strength across groups and individuals, in particular on receptive measures (e.g. picture-identification). This variation may be due to children's developing ability to benefit from cognates in such tasks, yet longitudinal studies of this phenomenon, especially with older children, are rare. Using longitudinal and cross-sectional analyses of picture-identification performance in French and English from 37 bilingual children attending a dual language program in France, this study investigates the cognate advantage across a wide range of ages (6-13 years old). The influence of children's relative exposure on the cognate advantage is also investigated. We find that significant differences in cognate versus non-cognate performance emerge only after the first years of elementary school. Children show marked growth in late elementary and middle school years, but only on the English task. The strength of the cognate advantage in picture-ID is inversely related to exposure to that language. These findings are discussed in relation to the nature of these children's exposure and properties of cognates in the two languages. Implications for dual language pedagogy are also discussed.