The National Rally was on 22.5 percent of voters' intentions, ahead of the ruling LREM party, on 21.5 percent according to the latest poll released by Ifop/Fiducial published on Thursday.
The elections on the 26 May will be a test for the French President, who has been facing a wave of protests at home, and a growing nationlist and eurosceptic sentiment across the member states.
Celebrating the 500 anniversary of the death of Leonardo de Vinci in Amboise on Thursday, President Emmanuel Macron reiterated his call for voters not to forget the "spirit of Europe".
"At a time when we're thinking about building Europe's future, we must remember that above all, Europe is made up of values, culture, intertwined destinies."
Earlier, on Tuesday, Macron called for a massive investment on behalf of his ministers and said Prime Minister Edouard Philippe would hold two or three meetings a week until the election.
Greens, Socialists far behind in polls
A separate poll by Opionway also showed the National Rally in front on 24 percent ahead of the LREM, allied with Modem on 21 percent.
Les Républicains (LR) were on 14 percent according to the same Opinionway poll.
François-Xavier Bellamy, leader of the LR criticised Macron, saying the fact that the LREM platform had not been unveiled one month ahead of the election "posed a significant democratic problem."
He called the government's approach one of "desired ambiguity", and that brandishing slogans was not enough.
Far behind them were European Green Party (EELV) on eight percent, on par with the far-left France Unbowed party.
The Socialist (PS)/Public Place (Place publique) list was at five percent.
20 percent of people interviewed did not respond to the questionnaire.
Campaigning slow to get off the ground
Marc Fesneau, the minister in charge of relations with the EU Parliament, said any poll results must be taken with a grain of salt.
"At this stage, this doesn't mean anything because French people are not yet in this campaign," he told Sud Radio.
He admitted however, that the elections would be tough.
He warned of "the forces at work in Marine Le Pen's party (RN) who want to destroy Europe."
National Rally leader Le Pen is in Sofia, Bulgaria on Friday to support the Nationalist party Volya which is launching their European Parliament election campaign.
The former secretary of the EELV explained why the campaigning was getting underway so late (9 May).
"Before this, it would've fallen on deaf ears, no-one wanted to discuss european election issues before this."
As for projected voter turnout, it has been decreasing since March, estimated at 39 percent, lower than the actual voter turnout of 42.4 percent, recorded in 2014.