France's economy minister Arnaud Montebourg was quoted by The BBC as saying that the government would block any deal it sees as unfit.
Montebourg said, "We are working to improve the offers to make sure that French companies...do not become prey.
"On the other hand we are open to alliances that help to equip us for globalisation."
Following the meeting president and GE chief executive Jeff Immelt said, "The dialogue was open, friendly and productive. It was important to hear in person President Hollande's perspective and to discuss our plans, our successful track record of investing in France, and our long-term commitment to the country.
"We understand and value his perspective, and we are committed to work together."
The meeting between Hollande and Immelt comes a day after Siemens made its offer for buying Alstom, which is one of France's major private sector employers.
Siemens' chief executive, Joe Kaeser will also meet Hollande and Montebourg to negotiate its offer of buying Alstom.
German engineering group Siemens has proposed paying Alstom half of its train-making business and some cash, BBC reported, citing French newspaper Le Figaro.
In return Siemens expects for Alstom's business that manufactures turbines for the power sector.
Since last decade, Alstom has experienced heavy debts and reduction in orders, while it was also bailed out by the French government in 2004.