It is claimed the US industrial giant will renege on a pledge to produce 1,000 new jobs by the end of the year.
Labour Minister Muriel Penicaud said GE would face a Euro 50,000 penalty for every job not created.
The move could be a test of President Emmanuel Macron's bid to push through more business-friendly policies, reports BBC.
GE had committed to create a net 1,000 new jobs by the end of this year when it bought the energy business of France's Alstom in 2014. The US company was in competition for Alstom with Siemens of Germany.
But GE had created only 323 jobs by the end of April, the Finance Ministry said last week.
GE chief executive John Flannery informed French Finance Minister Bruno Le Maire last week that the target was now "out of reach" because of difficult market conditions.
The minister urged GE to "take all necessary measures to comply to the best of its abilities".
On Sunday, Penicaud went further, telling BFM television: "The [Alstom] contract called for a Euro 50,000 penalty for every job not created."
According to Reuters, government spokesman Benjamin Griveaux, added: "Sanctions must set an example. Euro 50,000 should be applied by the end of the year if GE does not stick to its commitments."
While the sums involved are small for a company the size of GE - perhaps a total maximum of Euro 34m - the move runs counter to the government's bid to liberalise labour markets.
Macron, a former investment banker, has vowed to make France more attractive to foreign companies, pushing through reforms to make it easier for businesses to hire and fire workers.
The agreement to create the jobs was secured by France's previous Socialist government, and opposition parties are also now urging Mr Macron to apply the fine.
GE agreed to the job creation as part of its purchase of Alstom's power and electrical grid businesses, including its prized gas turbine operations, for EUR12.4bn (?10.8bn).
Shortly after the takeover GE announced plans to cut 6,500 power jobs in Europe because of falling oil and gas prices, and a further 12,000 job cuts in the sector were announced last December.
GE could not be reached for comment.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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