Economy Minister Arnaud Montebourg said last week that he plans a meeting with Immelt. A spokeswoman for Alstom, also a maker of railway rolling stock, had no immediate comment and could not confirm receipt of the letter.
Sources close to the French government on Saturday flagged a likely meeting between Montebourg and Immelt on Sunday. They said Prime Minister Manuel Valls might also meet the CEO, head of one of the world's 10 largest investor-controlled companies, should the more senior politician return from a visit to Rome in time. GE had no comment late on Saturday.
French media said last week that a decisive Alstom board meeting, the second since Friday, would also take place on Sunday.
Read MoreGE in talks to buy Alstom global power arm: Sources
Socialist Montebourg has been a strong exponent of France's traditionally cautious approach to foreign takeovers of companies in flagship industries.
Last week he said he would protect the national interest and study "other solutions and scenarios" for Alstom, also the maker of TGV high-speed trains and one of France's top private-sector employers, which is struggling with heavy debt and weak demand.
Speaking ahead of the Siemens statement amid intense speculation it would not stand idly by, one source close to the talks said the government had been looking for alternatives for months without success. "So I don't see what they will find now," the source said.
Deja vu Siemens
Political sensitivities about a French national champion run deep, and a deal with Siemens foundered partly because of them a decade ago when Alstom was rescued by a state-backed restructuring. The plan had been to swap of Alstom's power business with Siemens' rail business. French politicians see a GE deal in a similar light.
"I ask you, prime minister, to please tell the shareholders and management of the groups concerned that this transfer of control is out of the question," former Socialist minister Jean-Pierre Chevenement said in an open letter to Valls.
The source close to the talks said GE would argue there was not much concern about job cuts in France, where Alstom employs 20 percent of its workforce, about 18,000 people. The source noted that in gas turbines, for example, GE has its own turbine business in France while some of Alstom's is in Switzerland.
"The French state is asking for assurances from GE; all that is a game that implies a discussion around the disappearance of national champions," said the source. "Conversely, GE will try not to offer too much."
Sources have said a GE deal is backed by Alstom's main shareholder, French conglomerate Bouygues, which holds a 29 percent stake. Alstom's Kron told union officials on Friday he was discussing an "industrial operation" but did not name GE.
Bouygues and GE have declined to comment.