The European Commission said the deal would eliminate one of the three main competitors to GE in the market for heavy-duty gas turbines, potentially affecting customers in the 28-nation bloc.
"We are concerned that the proposed acquisition might not only lead to higher prices but also result in less choice for customers and less innovation in the sector," EU Competition Commissioner Margrethe Vestager said in a statement.
"Technology is and will continue to be crucial to help Europe meet its environmental commitments. Therefore, it is essential to maintain competition in the heavy-duty gas turbines market."
GE beat off fierce competition from German rival Siemens last year to seal the deal but then had to accept a working partnership with the French government in Alstom's associated nuclear, steam turbine, offshore wind and hydro power businesses.
It also had to hand over its train signalling operation to Alstom's high-speed rail unit, famous for its TGV trains, which will become the new core business of Alstom.
The French government demanded the concessions in response to a public outcry that one of the country's prized industrial giants would fall completely into foreign hands, costing jobs and damaging national prestige.
Under EU rules the Commission, the European Union's executive branch, has 90 working days, or until July 8 to make a final decision.