The deadline has been moved to June 23 from June 2. Alstom's board has given binding approval of the deal.
"We have done so to facilitate ongoing discussions with the government," GE said in a statement.
The company also repeated what CEO Jeff Immelt told analyst Wednesday at a conference, saying the deal is "good for Alstom, for France and for GE."
A company spokesman said GE views the extension as constructive and expects the conglomerate's deal team to be engaged in daily talks with the French government until the deadline. A rotating group of top executives, including Immelt, Vice Chairman John Rice and Steve Bolze, president of GE Power & Water, have been participating in the ongoing talks.
According to a person familiar with the situation, the government is concerned about four issues.
The first is how can GE help Alstom's transportation business. Alstom's power business is more profitable and its transportation business, which includes high-speed trains, could be vulnerable as a stand-alone. There are talks about Alstom buying or partnering with GE's signaling business.
Second, the government would like GE to would create joint ventures in the power business with other French companies.
Third, the government wants access to the nuclear technology of Alstom's power business and lastly, the government wants assurances jobs will not be lost.
GE's initial offer in April caught the French government by surprise and set off a political firestorm. The country's minister of Economy and Industry, Arnaud Montebourg, was an early and ardent critic of the deal, raising concerns about having a U.S. company acquire what is considered a French industrial jewel.
Last week, the government extended a decree that gives it the power to veto foreign takeover attempts in technology, defense and betting to the energy, transport, telecoms, water and health sectors as well.
The drama surrounding the bid, which would be the largest deal the company has attempted under Immelt, was a key topic Wednesday at GE's Electrical Products Group conference. Immelt was peppered with questions from analysts about whether GE might abandon the deal given the pushback it has received from the French government.
"You have to trust us a little bit that we know what we are doing," said Immelt. "We know how to do diligence, we know how to work with governments, we have an impeccable reputation in France. We are extremely experienced on this, that we know what we will and won't do in a very disciplined way and I think have thought all this through."
If approved, the deal would be accretive to GE and allow it to more quickly reach its goal of generating 75 percent of its earnings from its industrial operations and 25 percent from its finance arm. Since the financial crisis GE's been focused on reducing its dependence on earnings from GE Capital, which at one point accounted for half its profit.
—By CNBC's Mary Thompson.