Servisair, which handles baggages and passengers in several UK and European airports, recommended the Paris-based support services group's offer of 230p a share - a 15 per cent premium to Amey's 200p bid.
The appearance of the French white knight prompted several major shareholders in Servisair, including Schroders, Framlington and Standard Life, to sell their stakes.
Penauille was believed to be very close to the 50 per cent threshold last night, after buying around 29 per cent of Servisair's capital in the market and receiving undertakings for another 20 per cent. Servisair shares jumped 24.5p to 231p.
Amey refused to comment but insiders said that it was extremely unlikely to increase its bid. Other potential bidders, including the transport group Go-Ahead and the venture capitalist Compass were also considered out of the running.
John Willis, the Servisair chairman, said that the offer by Penauille, one of France's largest aiport services businesses, represented "good value for our shareholders and an excellent opportunity for... Servisair to develop internationally".
The deal will create a group with turnover of around pounds 450m and over 29,000 employees.
Mr Willis, who will remain in charge of Servisair's UK business, said the geographical fit was excellent as Servisair has no operations in France and Penauille needed to expand in the UK and the rest of Europe.
He said he did not expect any redundancies among Servisair's 5,000 staff.
The Servisair takeover is a victory for Jean-Claude Penauille, the chairman, chief executive and controlling shareholder of the French firm.
Mr Penauille has grown the company from a small cleaning firm into a company quoted on the Paris bourse with a market value of over pounds 200m and operations ranging from industrial cleaning to facilities management. The success by Penauille is a major blow for Amey, which wanted to acquire Servisair to boost its transformation from low-margin construction group into a high growth services company.