French has been at the Paperlinx subsidiary for three years in the role of division director for Sign & Display.
He has previously held roles at Xerox before becoming managing director of Spandex UK in 2001.
French said: "This is a really exciting opportunity and I am looking forward to leading this business as we navigate our way through the current trading conditions into what I believe is a period of growth and stability for this business.
"We have the potential to further enhance our products and services by fully developing the width and depth of our service to customers.
"Robert Horne is in a unique position in terms of our offer to market, from paper, board, plastics, pressroom consumables and packaging, through to wide-format machinery, environmental consultancy and waste management."