Recent theoretical models predict gains from international trade coming from intra-industry reallocations, due to a firm selection effect. In this paper we answer two related questions. First, what is the magnitude of this selection effect, and how does it compare to that of intra-national trade? Second, would the removal of ’behind-the-border’ trade frictions between integrated EU countries lead to large productivity gains? To answer these questions, we extend and calibrate the Melitz and Ottaviano (2005) model on productivity and trade data for European economies in 2000, and simulate counterfactual trade liberalization scenarios. We consider 11 EU countries and a total of 31 economies, including 21 French regions. Our first result is that, in the French case, international trade has a sizeable impact on aggregate productivity, but smaller than that of intra-national trade. Second, substantial productivity gains (around 20%) can be expected from ’behind-the-border’ integration. In both experiments, we predict the corresponding variations in average prices, markups, quantities and profits. We show that the model fits sales and exports data reasonably well, and we perform a number of robustness checks. We also suggest some explanations for the substantial cross-economy and cross-industry variations in our estimates of productivity gains, highlighting the importance of accessibility and competitiveness.