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We document how demand shocks in export markets lead French multiproduct exporters to reallocate the mix of products sold in those destinations. In response to positive demand shocks, French firms skew their export sales toward their best-performing products. We develop a theoretical model of multiproduct firms and derive the specific demand conditions (with endogenous price elasticities) needed to generate these product-mix reallocations. Under those demand conditions, the increased competition from demand shocks in export markets also induces productivity changes within the firm. We empirically test for this connection between demand shocks and the productivity of multiproduct firms. We find that this connection is economically substantial.