"Radio France has filed a complaint following the comments made by Mr. Jean-Luc Melenchon about Radio France journalists," the radio station said on Twitter.
The statement comes amid two separate investigations into possible misuse of European Parliament funds by Melenchon's France Insoumise ("Unbowed France") party and suspected irregularities in his 2017 presidential campaign funding.
Earlier this week, police raided Melenchon's Paris apartment as part of the probe.
The politician launched La France Insoumise in 2016 and also aimed for the presidency of the country. However, he did not qualify for the second round of voting, winning just 19% of the vote in the first round, placing fourth.