Le Pen is arguing that anonymity should be granted for the 500 signatures that any candidate for the presidency must obtain. Under current rules the signatories' names are published.
Under a 1976 French law, a candidate needs 500 signatures from elected officials in at least 30 different administrative departments across the country of in France's overseas territories.
The Constitutional Court will consider the matter on Thursday and will give its judgement the following Wednesday. The judges have the power to change the rules so that signatories' names can remain secret.
Le Pen herself said on Monday she had now received 400 signatures, although progress was slow.
"The signatures are arriving too slowly for our taste, but they are coming all the same," she said, reported Le Parisien newspaper on Tuesday.
"A certain number of mayors are aware that this situation is unacceptable and they need to be courageous," she added.
Her communications director agreed that they were "a little less pessimistic."
Help came from an unexpected quarter on Sunday when the centrist candidate, François Bayrou, suggested signatures could be transferred to Le Pen.
Bayrou is currently in fourth place in the opinion polls, just behind Le Pen. He said in a television interview that if she were to fall below the 500-signature barrier, the other parties "should discuss it."
Le Pen herself was in no mood to accept favours.
"I don't need to thank him," she said. "What's dramatic is that he's the only one to talk about this."
On Monday, one of the smaller candidates dropped out of the presidential race.
Christine Boutin, who leads the Christian Democratic party, said she was abandoning her presidential bid and would support Nicolas Sarkozy.
In particular, she cited his opposition to same-sex marriage, which she strongly opposes, as a key factor in her decision.
"I have led this campaign for nine months because I hold beliefs and values that are essential to our society," she wrote on her website.
Referring to the main opposition candidate, Socialist François Hollande, who says he will introduce same-sex marriage if elected, she said he "represents a danger for our country."