The FN gave Italy's Five Star Movement and the United Kingdom Independence Party (Ukip) the boost they needed to gather the 76 necessary signatures to trigger a confidence vote for next week.
The 44 signatures of the Europe of Freedom and Direct Democracy parliamentary group, which includes Five Star and Ukip, were bolstered by 32 names from other MEPs, including many from the FN.
"It is intolerable that a person who has been responsible for aggressive tax avoidance policies should serve as president of the European Commission," says the motion.
Juncker has come under fire over revelations that hundreds of multinational companies have avoided paying billions of euros in taxes to governments around the world under Luxembourg's tax schemes implemented when he was the country's finance minister and prime minister.
The confidence vote in the 751-seat legislature is likely to pass, however, with Juncker's centre-right European People's Party and the social-democratic group run by parliamentary president Martin Schulz both expected to oppose the motion.
The motion sees FN leader Marine Le Pen allying with Ukip leader Nigel Farage, who said during this year's European election campaign that the French far-right party "has anti-Semitism in its DNA".
Following historic advances in the May's European elections, the two parties ruled out working together and competed with each other to form a eurosceptic parliamentary group.
Ukip and Five Star went on to form Europe of Freedom and Direct Democracy, while the FN failed to win over the necessary number of parties to form a group under the parliament's rules.
The FN secured 24.96 percent of votes cast in the European elections in France, more than any other party.