The far-right party fired Leclere as a candidate in next year's local council elections after a TV documentary revealed that she had posted a photomontage of a baby monkey next to Taubira over the captions "18 months" and "now" on her Facebook page.
French human rights ombudsman Dominique Baudis has now written to the Paris prosecutors' office alerting it to an "incitement to discrimination, hatred or violence", which can mean a fine of up to 45,000 euros and up to a year in jail.
Taubira has decided not to take legal action herself and has not commented publicly on the montage.
Prime Minister Jean-Marc Ayrault on Friday expressed his "complete solidarity" with his minister, pointing out that Leclere was an FN parliamentary candidate in 2012.
Leclere herself on Friday claimed that the montage, of which she was not the author, "had nothing to do with racism" and was just "humour" but admitted that some of her statements in the documentary had been "clumsy".
She said she had received many messages of support but had been told to keep a low profile by the party's regional officials.
She is to face an Front National disciplinary committee.