A woman walks past electoral posters of French centrist presidential candidate Emmanuel Macron, right, and far-right candidate Marine Le Pen in Saint Jean de Luz, southwestern France, Wednesday, April 26, 2017.
The French investigation is aimed at establishing whether other sanctions are warranted.
Ms Le Pen's statement on Monday denouncing "the old and completely rotten Republican Front" - the coalition of mainstream parties allied against her - sums up her challenge in the May 7 run-off.
French Muslims overwhelmingly backed Socialist François Hollande at the last election in 2012; almost 90 percent chose him over the right-wing incumbent Nicolas Sarkozy. Le Pen has vowed to keep the Amiens plant open if elected, come what may.
The head of the Socialist Party says he will vote for Macron without hesitation and says his party will mobilise behind Macron's campaign.More news: Woman found trapped in hole inside Clinton County shed
She said she wanted to be "above partisan considerations" - with allies calling on those who backed the unsuccessful far-left candidate Jean-Luc Melenchon to continue voting "outside the system" by switching their support to Le Pen.
Her plans to restore France's borders with its European neighbours, pull out of the eurozone and hold a referendum on leaving the EU had sown fear of another devastating blow to the bloc after Britain's vote to leave.
While a financial scandal derailed the presidential bid of French conservative Francois Fillon, Le Pen, who is staunchly anti-EU, has so far survived the allegations unscathed.
The National Front leader is facing pro-European centrist Emmanuel Macron in France's May 7 presidential runoff.
The factory in Amiens, where the production of dryers is due to stop next year and shift to Poland, joins a list of threatened plants that have become symbolic of job losses in French presidential campaigns. "I will feel more free and above partisan considerations".More news: Murray loses to Thiem in Barcelona Open semifinals
The French presidential election could be greatly impacted by the immigration.
"This is the last French struggle, and we don't have much chance to defeat globalism and reverse the white genocide that is happening here, whether demographically or culturally", Electre, a French nationalist and activist, recently explained to AFP.
The contrasting images - on-the-spot action vs. a more formulaic approach - spoke to Le Pen's political smarts.
But she is seeking all the same to distance herself from the toxic legacy of her father and the xenophobic and anti-semitic undertones of his previous campaigns.More news: Turkey threatens further strikes on US-allied Syrian Kurds