The crisis kicked off last week when a video was posted on the National Front (FN) website in which Le Pen made an apparent anti-Semitic pun - the latest in a series of controversial statements by the 85-year-old who has had multiple convictions for inciting racial hatred and denying crimes against humanity.
As in previous instances, anti-racism campaigners were quick to condemn the remark. But this time, members of the FN itself also rose up in anger, including Le Pen's daughter Marine, who took over the party leadership in 2011.
And judging by the FN's triumph in European Parliament elections last month - when the party came first in France with 25 per cent of the vote - as well as its success in local polls in March, this strategy appears to be working.
Marine Le Pen's next task is to form and take command of a far-right grouping of parties in the European Parliament.
Also Read
She has so far secured the backing of Belgium's far-right Vlaams Belang (VB), the Dutch Party for Freedom (PVV), the Freedom Party of Austria (FPO) and Italy's Lega Nord, but is still short of the seven-nation representation required under EU rules to be considered a group.
In the video, Le Pen pledged to put his critics in their place - including French singer Patrick Bruel, who is Jewish - using a pun suggesting Nazi gas chambers.
FN vice president Louis Aliot, who is also Marine Le Pen's boyfriend, criticised it as "a bad phrase. It is politically stupid and dismaying."
Le Pen herself described the remark as a "political error", the first time that she has directly criticised her father in public.
He later tweeted: "I regret the statement made by the National Front president. It substantiates the slander I am a victim of.