ISG has paid £1.5m upfront for the business, with up to a further £5.9m due within two years depending on trading.
David Lawther, chief executive, said: “The Alpha acquisition is a key part of our continuing international expansion strategy and we are delighted to have acquired this capability within ISG.
“The acquisition will widen our international retail client base and provide a broader retail service offering to our clients in Europe.”
ISG’s existing European retail fit out firm will be integrated with the Paris-based Alpha business.
Alpha’s owner André Bernstein, who has 30 years of retail experience, becomes managing director of the combined European retail fit out business.
Alpha turned over around £6.5m last year and has a client base including Apple, Louis Vuitton, Uniqlo, Gucci, Tiffany & Co. and Patek Phillipe.
In addition to its core French market, Alpha has also delivered projects for clients in Italy and Switzerland.