By Ruth Bender and Christina Passariello 

PARIS--France's Moulin family, owner of upmarket store Galeries Lafayette, is moving down the food chain.

The Moulins said Monday that they have bought a 6.1% interest in Carrefour SA, the world's biggest retailer after Wal-Mart Stores Inc., through Motier Holding, their family investment vehicle.

The stake, worth EUR1.28 billion ($1.76 billion) based on Carrefour's closing share price of EUR29.16 Monday, makes the Moulins the third-largest shareholders in the supermarket chain behind private equity group Colony Capital LLC and the holding company of French businessman Bernard Arnault.

The firm said the investment in the French retailer is for the long term and "reflects its confidence in Carrefour's growth potential."

Motier bought the stake on the open market, a person familiar with the matter said.

Motier has a history in retailing: it was a partial owner of supermarket chain Monoprix for many years.

Galeries Lafayette sold its stake in Monoprix two years ago to Groupe Casino, Carrefour's main French rival.

A spokeswoman Carrefour declined to comment on the change in its shareholder structure.

Write to Ruth Bender at Ruth.Bender@wsj.com and Christina Passariello at christina.passariello@wsj.com

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