On 10 April French far-right leader Marine Le Pen participated in "Des Paroles et des Actes", one of the main TV debate shows in France. Facing her for the debate was MEP and leader of the centre-right UMP list for the EU elections, Alain Lamassoure, who had been invited to participate at the last minute.

Marine Le Pen's opponent of the night was supposed to be Martin Schulz, the current president of the European Parliament. However, according to the Coulisses de Bruxelles blog, the leader of the National Front (FN) said she would not take part if her opponent was a foreigner. The TV channel ultimately decided to withdraw the invitation to the German politician.

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The fact that France 2 bowed to her wishes triggered a lively debate. According to researcher and political scientist Joel Gombin "very few political leaders could afford this kind of luxury". It showed "how much the National Front has been de-demonised", he said.

De-demonisation – dédiabolisation – of the National Front, giving it wider political and social acceptance, is one of the cornerstones of Marine Le Pen's strategy.

Since she succeeded her father Jean-Marie Le Pen as new head of the party in 2011, she has been trying to drag the National Front towards the political mainstream. She wants to shed the party's image of being a movement of ageing bigots, anti-Semites and young skinheads. She herself is careful with her rhetoric and image, and has set about trying to prove that her generation is different from her father's.

De-demonisation means displaying "a certain distance to the main traditional markers of the far-right party, such as anti-Semitism," says Gombin.

This saw Marine Le Pen distance herself from controversial statements made by her father who once called the Nazi gas chambers "a detail of the history of world".

Another key strategy of hers is taking on board the traditional policies and values of political opponents, especially from the left-wing.

Since taking charge, Le Pen has moved the party to the left on social issues such as abortion and gay rights. And she did not campaign explicitly against gay marriage, which recently became legal in France.

The party has also increasingly taken a hard line on comments made by its members. It has excluded activists for explicit and public support for Nazism or for using racist and xenophobic language in public or on social media. There is also a handful of ethnic minority and younger candidates on the FN's list for the municipal and European elections.

A change in the party's DNA?

But what does this strategy actually say about a supposed ideological evolution? Has the DNA of the party really changed?

For Joel Gombin "de-demonisation" should be considered as "a story built up for the media".

"This strategy did not really start with Marine Le Pen," he says, noting that her father made similar ‘normalisation’ attempts.

But the main difference with previous attempts to de-demonise the party is that recently media "have taken up the concept of de-demonisation". In this respect, the researcher says that it has been successful. "Not so much for the reality it conceals, but because of the echo it has received in the media."

Yet, this strategy is ambiguous for more than one reason.

Last October, Anne-Sophie Leclere, a candidate for municipal election, provoked a storm by publicly comparing Justice Minister Christiane Taubira to a monkey.

On a TV show after the incident, Marine Le Pen noted she had "immediately suspended" the candidate. And Florian Philippot, the National Front's vice-president, said choosing Leclere had amounted to a "casting error".

But could they really have been ignorant of the fact that Leclere’s Facebook page was full of racial slurs? And, for each one who has been suspended, how many in the party are thinking and saying in private what Anne-Sophie Leclere said out loud?

That's the question journalist Claire Checcaglini asked herself when between May 2011 and January 2012 she infiltrated the National Front.

In a book published in 2013 Bienvenue au Front – Journal d’une infiltrée, [Welcome to the Front – Diary of an infiltrator], she writes: "With her quite appealing appearance, I thought that in the end Marine Le Pen may have attracted people with her de-demonisation speeches. But actually I found a lot of racist people who were relaxed about their racism."

Checcaglin noted that the economic and social issues raised by the National Front are rarely discussed among its supporters but that immigration is a key topic.

Other incidents support this finding. Last November, Nadia Portheault, a 26-year-old mother of Algerian background and head of the party's list in Saint-Alban, in the south west, left the party after hearing one party militant say: "You and your children are good for the oven."

"De-demonisation undoubtedly served its purpose by giving legitimacy to the National Front electorate and candidates," says Gombin.

But he says there has been "no major change" when it comes to the radical nature of the National Front electorate. And the party's voters still attach "huge importance" to the issue of immigration.

In addition, Marine Le Pen also makes controversial statements from time to time. Last October, for example, she remarked that she felt "uneasy" on seeing footage of the return of four French hostages who had been held by al-Qaida in Niger.

She said their behaviour and clothing – including their beards – were "surprising". "The two men had trimmed beards in a strange manner and their clothing was strange", she told French Radio Europe 1. "I think perhaps they need to explain all of that, it gives an odd impression to French people."

Le Pen is walking a political tightrope with the de-demonisation process as she tries to broaden the party's appeal while retaining its core supporters.

"The party needs to preserve its most precious political capital, the fact that the National Front is outside traditional political circles," says Gombin. If it becomes just like any other, it will lose "at least half of its electorate".

Recently, Marine Le Pen said she no longer wants the party to be described as "extreme right", and threatened to sue anyone who refers to the FN as such.

Her father brought similar lawsuits in 1995. The courts at the time refused even to consider his political arguments which distinguished between nationalism and populism on the one hand, and a xenophobic far- or extreme-right on the other.

As for Marine Le Pen, she has not carried out her threat so far. But the question has been keenly debated thus keeping her and her party in the media spotlight for weeks. And with less than a month to go to the EU elections, the party is leading in the polls.