When the leaders of France and Britain meet President Trump at the White House this week, they can draw on a well-worn playbook for dealing with their mercurial host. But it is not clear that the old tricks will be enough to meet the new challenge.

After a week in which Mr. Trump branded President Volodymyr Zelensky of Ukraine as a dictator, President Emmanuel Macron of France and Prime Minister Keir Starmer of Britain are no longer merely navigating a norm-busting president with a distaste for multilateral institutions and decorous diplomacy.

They are also trying to salvage a trans-Atlantic alliance that has fallen into existential crisis.

Mr. Trump’s hostile statements, coupled with his overture to President Vladimir V. Putin of Russia to go over Europe’s head to strike a peace settlement in Ukraine, have left some Europeans wondering whether the alliance that protected the continent for more than seven decades is already defunct.

So inviting Mr. Trump to a French military parade, as Mr. Macron did on Bastille Day 2017, or to a lavish banquet at Buckingham Palace, as Queen Elizabeth II of Britain did in June 2019, might not be sufficient to get things back on track.

“This is the moment of truth,” former Prime Minister Malcolm Turnbull of Australia said in an interview. “They simply have to have the steel to stand up to Trump and tell him what they think, namely, that siding with Putin against Ukraine is a devastating blow to America’s prestige and standing in the world.”

Mr. Turnbull, who had his own clashes with Mr. Trump over refugees early in the president’s first term, said that efforts to charm or cajole him on an issue this fundamental would likely go nowhere. “If the price of getting along with Trump is abandoning your allies, that is too high a price to pay,” Mr. Turnbull said.