The graffiti was discovered in one of the French capital's metropolitan trains on Tuesday, prompting the International League against Racism and anti-Semitism (LICRA) to file a complaint.
The authors of the graffiti have yet to be identified.
"The LFP will join the lawsuit initiated by LICRA against the authors of this graffiti," the LFP wrote in a statement.
"The LFP condemns the racist, anti-Semitic and homophobic graffiti targeting Kylian Mbappe."
Mbappe, whose father is from Cameroon and whose mother is of Algerian origin, was born in Paris.
The 20-year-old striker was one of the heroes of France's victorious World Cup campaign in Russia last year, scoring their fourth goal in their 4-2 win over Croatia in the final.
(Reporting by Julien Pretot; Editing by Toby Davis)
