PARIS — The one-on-one duel that has shaped French political life for nearly a decade ratcheted up a notch last week, with the far-right leader Marine Le Pen claiming one big scalp, and giving notice of going after a bigger one, President Emmanuel Macron.

No one doubted that she was calling the shots. Yet by Monday, Mr. Macron had relegated Ms. Le Pen and her party, the anti-immigrant National Rally, to “pariah” — her word — status. He did not deign to meet with her in his search for a new prime minister to replace the one she had largely ousted last week.

Leaders of other parties had tête-à-têtes with Mr. Macron at the presidential palace; but not Ms. Le Pen, who was excluded because she is part of the “anti-Republican front” — his words.

That could turn out to be a big mistake. Last week, Ms. Le Pen announced the demise of the hapless prime minister, Michel Barnier, in Parliament; sure enough he was overthrown in a no-confidence vote soon after.

Mr. Barnier had tried to force through a budget proposal without a vote, and above all he had barely consulted with Ms. Le Pen, who has the largest bloc of parliamentarians and cannot be ignored.

She has suggested successive Macron governments could fall, until he steps down — making clear she is after a more consequential trophy: the president himself.