French industry minister Arnaud Montebourg sent a letter to GE chief executive Jeffrey Immelt stating that he wished to see a "more balanced partnership".
Siemens has proposed an alternative deal that would see it take on Alstom's energy business in return for transferring part of its train division to Alstom to create "two European champions".
According to French paper Les Echos, the letter reads: "As it stands, we cannot agree with the proposals you made based solely on the acquisition of Alstom's activities in the field of energy."
Instead of the suggested deal, which Montebourg suggests would "lead to Alstom's disappearance", the letter proposes a 50:50 joint venture similar to the one set up between GE and French aerospace company Safran.
Alstom's energy business accounts for around 70% of its revenues, and Montebourg wrote that its train business alone would be too small to compete on the global market.
The French government has wide ranging powers to block takeovers of French companies and is often vocal in its opposition to moves by foreign firms to buy key French businesses.
Following the tabling of a EUR 12.35 billion ($16.9 billion) deal by GE in April, Alstom said that it "acknowledged unanimously the strategic and industrial merits of this offer". It has set up a committee of independent directors to review the offer before the end of May.
A takeover by GE would have significant consequences for the wind industry, with two major players merging. If Alstom opts to go with GE, it could have awkward repercussions for Alstom's burgeoning offshore business, given the US company's antipathy to the sector.
Earlier this year, GE renewables chief Anne McEntee restated that the company had no plans to enter the offshore market.