The proposed deal would be for the thermal, renewable and grid sectors of Alstom's energy business. It stated that it would now review the bid before the end of May and, if completed, would use the cash to strengthen its transport arm.
Alstom's shares have been suspended on the Paris stock exchange since last Thursday. When they resumed trading Wednesday morning, they jumped 11 percent to nearly 30 euros.
Jeff Immelt, GE Chairman and CEO, said that the potential tie-up is expected to provide an excellent return on capital and advances the U.S. company's strategic priorities and industrial growth.
"We respect and value the deep industry and technology expertise of Alstom employees and expect them to add to our proven track record of developing talent and leadership in France and globally," Immelt said in the press release. Patrick Kron, Chairman and CEO at Alstom added that the deal would create a more "competitive entity" and Alstom's employees would join a well-known, major global player.
The bid has already been the subject of top-level political discussions at the heart of the French government, and may still be gatecrashed by Germany's Siemens.
French Prime Minister Manuel Valls told news agencies Wednesday that Alstom had yet to make a final decision on which bid to accept and would discuss the deal with the government before making a final decision.
As part of the GE's bid, Alstom said that it may not solicit offers from third parties for the acquisition of its energy business. However, it has reserved the right to respond to unsolicited offers in what looks like a direct nod to the interest from Germany's Siemens.
It is also considering a declaration of interest from Siemens, but has not yet received a formal offer from its German rival. Siemens has been allowed access to Alstom's financial information and has highlighted its interest in the firm. On Tuesday afternoon, Siemens said that it would carry out suitable due diligence before logging a more binding offer.
The French government has paid close attention to the ongoing saga surrounding Alstom. Immelt met French President Francois Hollande on Monday to discuss the U.S. company's bid but French officials have also courted the rival proposal from Siemens.
Initial communications from the German company suggest that it is willing to offer more safeguarding of French jobs and that it has offered to contribute "significant" parts of its rail systems business to Alstom, helping it to become a "global champion".
GE sought to allay fears over jobs too, saying it anticipated net growth in jobs in acquired businesses in France, with the employee mix moving toward high value manufacturing and engineering jobs.
General Electric CEO Jeff Immelt will join CNBC for a First On interview at about 0930 EST/1430 BST.