During a speech in Paris, party leader Marine Le Pen urged voters to seize the May 26 vote as a chance to "beat" French President Emmanuel Macron after weeks of anti-government protests.
"The moment of the big political changeover has come," Le Pen said of the hoped-for wins by nationalist movements like hers.
"What we propose is a quiet transition from the European Union to the European alliance of nations...that will allow us to reconquer our border control, our legislative, budget and monetary sovereignty", she said.
National Rally's campaign slogan was unveiled in giant letters at Sunday's meeting: "We're coming."
Le Pen suggested the yellow vest protests against Macron's economic policies during the last two months could help her populist party at the ballot box. The movement started to oppose fuel tax increases but expanded to challenge government policies seen as favoring the wealthy.
The movement appeared to gain new momentum this weekend. The French Interior Ministry said about 84,000 people turned out on Saturday for the ninth straight round of demonstrations across Franc, up from 50,000 the previous week.
"Today, it's inevitable that the yellow vests are part of the national context and will influence, of course, the elections," National Rally activist William Courtin said at the party meeting. "In our favor, I hope."
The French president's office issued a "letter to the French" from Macron on Sunday evening. He explained how he planned to address the yellow vests movement's concerns through a three-month "grand debate" taking place through meetings in all the country's regions starting this week.
"That's how I want to turn angers into solutions with you," he wrote.
The French leader said the debate would help the government develop policies and France's position on the European and international scene.