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The meeting between the French head of state and the boss of one of the world's 10 largest publicly-quoted corporations follows a weekend of political and corporate drama, in which Alstom's German rival Siemens proposed a swap of assets to counter a potential Alstom-GE tie-up. GE CEO Jeff Immelt arrived at the presidential palace at 0720 GMT - flanked by Clara Gaymard, the head of GE France - and said "bonjour" to reporters before entering the Elysee.
Hours before the meeting, Montebourg said France would block any deal it considered unsuitable in terms of the long-term interests of the French company, its employees and the economy.
But he stopped short of calling for Alstom's nationalisation if neither GM's offer nor a rival one from Germany's Siemens proved acceptable.
Montebourg and Hollande will also meet with Siemens' CEO Joe Kaeser, he added. This will then be followed by a meeting with Martin Bouygues, the billionaire chairman of family conglomerate Bouygues, Alstom's largest shareholder with a 29.4 percent stake.
"We are working to improve the offers to make sure that French companies ... do not become prey," Montebourg told RTL radio. "On the other hand we are open to alliances that help to equip us for globalisation.
"For the time being we are in discussions with two parties, General Electric and Siemens. They have two offers that would allow to adopt different industrial strategies."
Immelt arrived in Paris aiming to hammer out a $13 billion deal to buy Alstom's power turbines business, after news of talks between the French trains-to-turbines group and the U.S. industrial and financial group late last week.
His arrival coincided with French political uproar over the potential loss of a national champion and the emergence of a rival proposal involving Siemens.
Meetings at the Elysee with Siemens and Bouygues were respectively scheduled for 1600 GMT and 1715 GMT on Monday.
ASSET SWAP
The German company, like Alstom, makes high-speed trains and other rolling stock as well as power station turbines, and is proposing a swap of assets that would make Alstom a more significant rail transport player while enhancing its own turbines and power grid equipment business.
Alstom needs a partner one way or another. Suffering from heavy debts and a downturn in orders, it was bailed out by the French government in 2004. Sources familiar with the GE-Alstom talks that came to light late last week say they have been going on for months and are very advanced.
Montebourg, who threatened to nationalise blast furnaces belonging to steelmaker ArcelorMittal when its owner tried to shut them down, said the Siemens proposal would create "two European and global champions".
And he warned that the government on which Alstom relies for much of its business would not accept the sale of Alstom's power business - especially the sensitive nuclear portion - in haste.
Asked if he could seek to temporarily nationalise Alstom if neither offer proved suitable, Montebourg told RTL: "It's too early to raise that question."
Labour Minister Francois Rebsamen, asked if nationalisation remained an option, told France Inter radio: "I think nothing is out of the question at the moment."
GE has declined to comment throughout. Alstom has also declined to go into detail about its discussions, but said in a statement on Sunday it would ask for a suspension of its shares until Wednesday while it considers its options. Siemens said on Sunday it had written a letter to Alstom about strategic opportunities but also did not go into detail.
Alstom shares, which had slumped earlier this month to a near nine-year low, jumped at the end of last week to reach their highest in five months.
