The parliament suspects the money went to FN assistants who were not really working for MEPs, but were engaged in FN party work in France.
The allegations - denied by the FN - have now gone to French investigators.
Ms Le Pen is campaigning for the second-round vote in the presidential election on 7 May. Her rival, liberal centrist Emmanuel Macron, is ahead of her in opinion polls.
The alleged fraudulent payments - from 2012 onwards - concern her and several other FN MEPs. The FN is highly critical of the EU, rejecting its liberal, free market agenda.
Parliamentary immunity
Ms Le Pen says she is the victim of a politically motivated vendetta.
The European Parliament is currently withholding half of Ms Le Pen's salary and expenses, as it tries to recoup money it says she owes.
Currently the FN has 24 MEPs, France's biggest contingent.
Ms Le Pen has refused to answer a summons over the affair in France, citing her immunity as an MEP.
The BBC's Hugh Schofield in Paris says most voters drawn to the FN are already highly suspicious of the EU, and may not see the alleged fraud as a particularly serious matter.
Holocaust controversies
On Tuesday Ms Le Pen stepped aside as FN leader, saying she needed to be above partisan considerations in the presidential election.
The FN's new temporary leader is Jean-François Jalkh, and he has immediately been caught in a row over a 2000 interview, in which he is quoted as doubting the Nazis' use of Zyklon B cyanide gas to murder Jews and other victims in the death camps.
"I consider it technically impossible - I repeat, impossible - to use it... in mass murder. Why? Because you have to wait several days before you can decontaminate a place where Zyklon B was used," Le Monde quoted him as saying.
When Le Monde asked him about the remark he called it "utter rubbish" and said he had "no recollection of that [interview]".
A year ago the FN's founder, Jean-Marie Le Pen, was fined €30,000 (£25,278; $32,600) for calling the Nazi gas chambers a "detail" of World War Two.
He was convicted of contesting crimes against humanity. He got the same conviction in 2012 for calling the Nazi occupation of France "not particularly inhumane".
Marine, his daughter, drew strong criticism on 9 April when she suggested France was not responsible for a 1942 wartime round-up of 13,000 Jews, who were sent from France to Nazi death camps.
More about: #LePen #Frenchelections
