"In its current form, we can unfortunately not agree to the propositions you have made, resting only on the acquisition of Alstom's activities in the energy sector," Economy Minister Arnaud Montebourg said in a letter to GE chief Jeff Immelt.
The US behemoth has been vying for Alstom's energy assets with German giant Siemens in a politically sensitive bidding war over the French engineering group.
Montebourg was charged by French President François Hollande with responding to GE's €12.4 billion ($17 billion) bid for the energy assets of the company, which employs 18,000 staff in the country.
The firebrand minister has vowed to "defend the industrial interests of the nation" in the deal.
In the letter seen by AFP, Montebourg told Immelt the French government "wishes to examine the ways and means of a balanced partnership, rejecting a pure and simple acquisition that would lead to the demise of Alstom."
He said the French government was concerned about "the separation and isolation of the branch of Alstom specialized in rail transport" if GE only buys the energy arm.
Energy activities — which include power generation and transmission — account for about 70 percent of Alstom's business but the company is better known as a railway equipment maker that manufactures France's prized TGV high-speed trains.
Montebourg suggested that General Electric in turn hand over its activities in the rail sector to Alstom.
"It would be highly desirable to insure a global future for Alstom Transport, by ceding General Electric's transport activities to this entity, including freight trains and signals, representing revenues of $3.9 billion," the minister said.
Reacting to Montebourg's letter, General Electric defended its bid for Alstom's energy assets.
"We appreciate the engagement of the French government. We believe our proposal is good for France, for Alstom and for GE. As our letter to President Hollande stressed, we are open to continuing dialogue," said the company.
Shares in GE, a Dow component, closed at $26.58, down 0.4 percent.