MARSAZ, France—Nestled in the hills of central France, Louis Vuitton's new factory—inaugurated Friday—expands the luxury label's production capacity by 70 people, a drop in the bucket for the brand, which has annual sales of €5 billion ($7.09 billion) and employs about 3,500 leather-goods workers in France alone.

The site is part of a strategy to eke out small quantities of growth throughout its operations, starting with the factory floor. Vuitton's size means it has fewer unexplored avenues to tap for growth than competitors.

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