Pictures of the Parc OL stadium showed that seats had been ripped up and the LFP blamed the PSG supporters.
"The LFP firmly condemns the behaviour of a section of the PSG fans at Parc OL," the LFP said in a statement on Sunday.
PSG won the game 4-1 to clinch their fourth successive League Cup title.
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"As soon as next Thursday, the LFP's disciplinary commission will look into the case," the statement added.
(Reporting by Julien Pretot; Editing by Clare Lovell)
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