PARIS--The French government has reached an agreement to purchase a stake in Alstom SA from its leading shareholder, Economy Minister Arnaud Montebourg said Sunday, clearing the way for General Electric Co. to complete its acquisition of most of the French industrial firm.

The accord--hashed out in marathon talks between the government and French conglomerate Bouygues SA--grants the government an option to buy as much as 20% of Alstom from Bouygues at a future date, Mr. Montebourg said.

Bouygues, whose businesses range from construction to telecommunications, said the government's option to buy Alstom shares will last for 20 months and begin after the GE-Alstom deal closes. Under the agreement reached Sunday, the government can buy shares held by Bouygues at a discount to their market rate, with a floor price of about EUR35 ($47.60), Bouygues said.

"We reached an agreement with Bouygues," Mr. Montebourg told French TV. The minister added that the government would move to purchase the stake when Alstom shares were trading at their "lowest" levels on the stock market.

The share-purchase agreement removes the final hurdle from GE's pursuit of Alstom. The French government had warned that it wouldn't sign off on GE's acquisition until the government bought most of Bouygues's Alstom stake.

Paris is intent on becoming Alstom's biggest shareholder to strengthen its grip on the maker of power equipment and bullet trains. Alstom will emerge from the GE acquisition as an equal partner in a series of joint ventures that employ thousands of people in France and produce politically sensitive technology, such as turbines for nuclear plants.

But the government's decision to purchase the stake at a future date--and after markets have time to react to GE's acquisition of Alstom's assets--marks a concession that could make buying the stake more costly for the French state at a time when it is struggling to meet budget targets approved by the European Union.

Paris had previously insisted on paying Alstom's core shareholder Bouygues a maximum of EUR28 a share, the stock's closing price on the Paris Bourse on Friday, according to people familiar with the matter. Bouygues, which is seeking to raise cash to finance a restructuring at its telecom unit, was seeking a significant premium over Alstom's last trading price, people familiar with the matter said.

On Saturday, Alstom's board said it had officially accepted GE's sweetened offer for its power-equipment unit, leaving the government's haggling with Bouygues as the only obstacle to the GE-Alstom deal.

The U.S. company on Friday changed its $17 billion initial offer for the whole of Alstom's power business to make it more palatable to the French government, which has been reluctant to let the industrial jewel fall into U.S. hands and potentially threaten French jobs.

GE revised its bid to give the France more say in Alstom's future. Alstom would sell its gas-turbine business, the largest part of the power-equipment unit, to the U.S. company. But it also would house the French part of its steam- and nuclear-turbines operations, renewable-energy activities and grid-equipment business in 50/50 joint ventures with GE. The board said the new offer benefits Alstom, its shareholders and other stakeholders.

The new GE offer still values the power-equipment business at $17 billion, but values the Alstom investment in the joint ventures at EUR2.5 billion ($3.4 billion), the Alstom board said Saturday.

After the transaction, Alstom will buy GE's train-signaling business and merge it with its own train business, which makes France's signature bullet trains. Alstom intends to focus on its train business in the future, the board said.

Write to Stacy Meichtry at stacy.meichtry@wsj.com and Inti Landauro at inti.landauro@wsj.com

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