The combined group will be the sixth-largest contractor in Europe with turnover of pounds 4.7bn and 48,000 employees.
Initially, Amec is paying pounds 20m-pounds 23m for a stake of between 40 and 48.6 per cent in Spie with the remainder of the shares acquired by management and employees. But it has an option in six years to take full control by buying out the other shareholders.
Amec and the Spie employees will pay the owners of the business, Schneider, pounds 40m in cash. Spie has also agreed to buy out Schneider's 50 per cent stake in the electrical services business Spie Trindel for pounds 75m.
The deal follows Kvaerner of Norway's unsuccessful bid for Amec and Amec's failure to merge with fellow UK contractor, MacAlpine.
Peter Mason, chief executive of Amec, said: "Europe is the largest construction market in the world and it is beginning to consolidate. In the long term there will only be half-a-dozen contractors left in Europe. If we don't do something we will be left behind and there won't be a UK player in that premier league."
Amec employs 20,000 and with turnover of pounds 2.7bn is a big player in the oil and gas and rail markets and building and civil engineering.
Spie, one of the 10-strong consortium that built the Channel Tunnel, is France's fifth-biggest contractor specialising in electrical and civil engineering construction and pipe laying. It has 28,000 employees and sales of pounds 2bn a year.
In recent years, Spie's trading performance has been affected by a number of problem contracts and its exposure to property development. Last year it made pre-tax profits of pounds 4m and this year Amec said it would be profitable at the trading level.
But the property division, together with liabilities relating to a number of construction contracts and Spie's North American interests are being retained by Schneider. Spie has net cash of Fr1.2bn (pounds 137m).
Amec said the acquisition would give it greater access to European and international markets, particularly France where construction output is forecast to grow by 0.4 per cent in 1997 after several years of decline.