The growth in studies on business data has revealed the wide differences in productivity between firms, sometimes even within narrowly defined activity sectors. The least productive firms therefore have ample margin for catching up. Their convergence towards the level of the most productive firms can be an important factor in productivity dynamics at macroeconomic level. Our article sheds light on this convergence in France in the 1990s and 2000s, and on some of its possible determinants. Convergence was greater for labour productivity than for total factor productivity. But, most importantly, the speed of convergence slowed in the 1990s, mainly because of an acceleration in the productivity of firms on the technological frontier, i.e., the firms that were already the most productive. We suggest three explanations for these stylized facts: (1) globalization and (2) information technologies, which seemingly benefited the most productive firms, and (3) increased competition, which stimulated the productivity of firms on the technological frontier while inhibiting convergence for the least productive firms.