After a meeting between French President Francois Hollande and GE head Jeffrey Immelt, the source said that "General Electric has undertaken to create 1,000 jobs in France."
Referring to a counter offer from German group Siemens, a French presidential source said: "We are working in the context of two proposals."
General Electric is offering 12.35 billion euros ($17.0 billion)to buy the power business of Alstom which is also a leading manufacturer of rolling stock for railways including the French TGV high-speed train.
But when the advanced stage of these talks with Alstom emerged, the government expressed alarm that control of Alstom's power industry, including some nuclear power activities, would move to the United States and that jobs would be lost.
GE already has big manufacturing activities in France, some of them next to Alstom production lines.
Alstom, which faces financial strains, had already put part of its rail activities up for sale.
The company considers that it is too small on the world market for power-generating turbines but could be the world leader in the rail sector, and has sent strong signals it prefers a deal with GE.
The government then encouraged German industrial group Siemens to make a counter offer, and Siemens is interested in acquiring the power business in exchange for handing Alstom its own rail division.
Siemens values the power activities, representing about 70 percent of Alstom's business, at 10.5-11.0 billion euros.
The proposed GE jobs would be in the industrial sector, the French source said on Wednesday after the second meeting between Hollande and Immelt.
This highlighted a central policy push by the Socialist government to stop a decline of French industry and reduce record high unemployment which was a factor in the latest drubbing for the Socialists in European elections on Sunday.
Earlier, sources close to the French president had said: "Today it is possible to see that the offer from General Electric is becoming clearer, has been improved, strengthened, notably concerning employment."
Last week GE extended the life of its offer by three weeks until June 23 to allow time to win over the French government.