French family policy has always provided specific support to families with three or more children, over the period 1978-1982 in particular. The authors discuss the effectiveness of this policy by comparing fertility at birth order three and above in France and western Europe and by observing changes in the proportion of mothers of two children who have progressed to a third child (parity progression ratio A2) since the 1970s. They show that targeting policy on the third child did indeed influence the frequency of these births, but that this influence is limited and difficult to quantify. The article then focuses on the characteristics associated with the parity progression ratio A2. The PPR is most strongly influenced by age at second birth, the length of the interval between the second and third births and nationality. All the other variables examined – sex of first two children, parents’ sibship size, union history, mother’s occupational history, educational attainment and socio-occupational category of each partner – are significant, even after controlling for structural effects. Recent tendencies, notably the increase in age at second birth, point to an ongoing downward trend in the probability of having a third child.