Do tariffs inhibit trade flows by limiting the entry of exporting firms ('extensive margin') or by restricting the average volume exported by each firm ('intensive margin')? Using a gravity equation approach, we analyze how the decrease in tariffs promoted during the 1990s by the Uruguay Round multilateral trade agreement affected the trade margins of French firms across 57 sectors and in 147 countries, from 1993 to 2002. Our main contribution is to estimate the elasticity of trade for both margins, controlling for the unobserved heterogeneity of trade flows thanks to a three-dimensional panel and to time-varying tariffs as a measure of variable trade costs. Our results show that the number of firms exporting in a given sector to a given destination is related to the level of tariffs. But they also show that the decrease in tariffs determined by the implementation of the Uruguay Round did not lead more firms to export and instead, only encouraged incumbent exporters to increase their shipments. We control for two problems that may affect our basic specification: tariff changes may be endogenous and zero flows are not included. Our results are confirmed - even when the extensive margin is significant, its contribution is very small.