The valuations and terms of the agreement were not immediately available.
"The deal is done. A formal announcement is expected shortly," one of the sources said. Media reports have valued Fabindia, a retail chain which sells garments, furnishings, fabrics and ethnic products, at about 14 billion rupees ($283 million).
Wolfensohn Capital Partners, the New York-based venture capital fund of former World Bank President James Wolfensohn, bought the stake in the Indian chain in 2007 for about $10 million.
Fabindia, also plans to raise funds for expansion, the sources said.
Sanjiv Kapur, managing director of Wolfensohn India, and a spokeswoman for Fabindia declined to comment, while L Capital Managing Director Sanjay Gujral did not immediately respond to an email seeking comment.
L Capital Asia launched a $640 million fund last year targeting emerging economies including China and India.
The French fund last year bought 25.5 percent stake in India's Genesis Luxury Fashion Pvt Ltd, which distributes global luxury brands, mainly apparel and accessories. (Reporting by Indulal PM; Editing by Harish Nambiar)