PARIS — Most countries lost patience long ago. The erratic outbursts of President Trump were unacceptable to allies when they were not simply insulting. Even rivals like China and Russia reeled at the president’s gut-driven policy lurches. Mr. Trump said in 2016 that America must be “more unpredictable.” He was true to his word.

The sudden infatuation with North Korea’s Stalinist leader, Kim Jong-un, the kowtowing to President Vladimir V. Putin of Russia, the “Chinese virus” obsession, the enthusiasm for the fracturing of the European Union, and the apparent abandonment of core American democratic values were so shocking that Mr. Trump’s departure on Wednesday from the White House is widely viewed with relief.

The sheen is off America, its democratic ideals hollowed. Mr. Trump’s imprint on the world will linger. While passionate denunciations are widespread, there is a legacy of Trumpism that in some circles won’t easily fade. Through his “America First” obsession, he galvanized other nations to put themselves first, too. They will not soon fall back into line behind the United States. The domestic fracture that Mr. Trump sharpened will endure, undermining the projection of American power.

“Mr. Trump is a criminal, a political pyromaniac who should be sent to criminal court,” Jean Asselborn, Luxembourg’s foreign minister, said in a radio interview. “He’s a person who was elected democratically but who is not interested in democracy in the slightest.”

Such language about an American president from a European ally would have been unthinkable before Mr. Trump made outrage the leitmotif of his presidency, along with an assault on truth. His denial of a fact — a defeat in the November election — was seen by leaders including Angela Merkel, the chancellor of Germany, as the spark to the Jan. 6 storming of the Capitol by Trump supporters.

A mob amok in the inner sanctum of American democracy looked to many countries like Rome sacked by the Visigoths. America, to foreign observers, has fallen. Mr. Trump’s reckless disruption, in the midst of a pandemic, has bequeathed to Joseph R. Biden Jr., the incoming president, a great global uncertainty.

“The post-Cold War era has come to an end after 30 years, and a more complex and challenging era is unfolding: a world in danger!” said Wolfgang Ischinger, the chairman of the Munich Security Conference.

Mr. Trump’s talent for gratuitous insults was felt the world over. In Mbour, a coastal town in Senegal, Rokhaya Dabo, a school administrator, said, “I don’t speak English, but I was offended when he said Africa is a shithole.” In Rome, Piera Marini, who makes hats for her store on Via Giulia, said she was delighted Mr. Trump was going: “Just the way he treated women was chilling.”

“Biden needs to tackle the restoration of democracy at home in a humble way that allows Europeans to say we have similar problems, so let’s get out of this together,” Nathalie Tocci, an Italian political scientist, said in an interview. “With Trump, we Europeans were suddenly the enemy.”

Still, to the last, Mr. Trump’s nationalism had its backers. They ranged from the majority of Israelis, who liked his unconditional support, to aspiring autocrats from Hungary to Brazil who saw in him the charismatic leader of a counterrevolution against liberal democracy.

Mr. Trump was the preferred candidate of 70 percent of Israelis before the November election, according to a poll by the Israel Democracy Institute. “Israelis are apprehensive about what lies beyond the Trump administration,” said Shalom Lipner, who long served in the prime minister’s office. They have their reasons. Mr. Trump was dismissive of the Palestinian cause. He helped Israel normalize relations with several Arab states.

Elsewhere the support for Mr. Trump was ideological. He was the symbol of a great nationalist and autocratic lurch. He personified a revolt against Western democracies, portrayed as the place where family, church, nation and traditional notions of marriage and gender go to die. He resisted mass migration, diversity and the erosion of white male dominance.

One of Trump’s boosters, the nationalist Brazilian president, Jair Bolsonaro, claimed this month that in the American election, “There were people who voted three, four times, dead people voted.” In an illustration of Mr. Trump’s role as an enabler of autocrats, Mr. Bolsonaro went on to question the integrity of Brazil’s voting system.

Viktor Orban, Hungary’s anti-immigrant prime minister and a strong Trump supporter, told Reuters last year that the Democrats had forced “moral imperialism” on the world. Although he congratulated Mr. Biden on his victory, Mr. Orban’s relations with the new president are certain to be strained.

This global cultural battle will continue because the conditions of its eruption — insecurity, disappearing jobs, resentment in societies made still more unequal by the impact of Covid-19 — persist from France to Latin America. The Trump phenomenon also persists. His tens of millions of supporters are not about to vanish.

“Were the events at the Capitol the apotheosis and tragic endpoint of Trump’s four years, or was it the founding act of a new American political violence spurred by a dangerous energy?” François Delattre, the secretary-general of the French Foreign Ministry, asked. “We do not know, and in countries with similar crises of their democratic models we must worry.”

France is one such country of increasingly tribal confrontation. If the U.S. Justice Department could be politicized, if the Centers for Disease Control and Prevention could be eviscerated, and if 147 elected Members of Congress could vote to overturn the election results even after the Capitol was stormed, there is reason to believe that in other fractured post-truth societies anything could happen.

“How did we get here? Gradually and then suddenly, as Hemingway had it,” said Peter Mulrean, a former United States ambassador to Haiti now living in France. “We’ve seen the steady degradation of truth, values and institutions. The world has watched.”

As Simon Schama, the British historian, has observed, “When truth perishes so does freedom.” Mr. Trump, for whom truth did not exist, leaves a political stage where liberty is weakened. An emboldened Russia and an assertive China are more strongly placed than ever to mock democracy and push agendas hostile to liberalism.

Toward China, Mr. Trump’s policy was so incoherent that Xi Jinping, the Chinese leader, was left appealing to Starbucks, which has thousands of stores in China, to improve strained U.S.-China relations. Mr. Xi wrote last week to the company’s former chief executive, Howard Schultz, to “encourage him” to help with “the development of bilateral relations,” the official Xinhua news agency reported.

Mr. Xi no doubt feels some Trump whiplash. The president once called him just “great,” before changing his mind. China, after negotiating a truce in the countries’ trade war a year ago, came under fierce attack by the Trump administration for enabling the virus through its initial neglect and for its crackdown in Hong Kong. The administration also accused the Chinese government of committing genocide in its repression of Uighurs and other Muslim minorities in the Xinjiang region of China.

Mr. Trump’s approach was erratic but his criticism coherent. China, with its surveillance state, wants to overtake America as the world’s great power by midcentury, presenting the Biden administration with perhaps its greatest challenge. Mr. Biden aims to harness all the world’s democracies to confront China. But Mr. Trump’s legacy is reluctance among allies to line up behind a United States whose word is now worth less. It seems inevitable that the European Union, India and Japan will all have their own China policies.

Even where Mr. Trump advanced peace in the Middle East, as between Israel and some Arab states, he also stoked tensions with Iran. Mr. Biden has suggested that President Abdel Fattah el-Sisi of Egypt was Mr. Trump’s “favorite dictator.” But then America is no longer the world’s favorite democracy.

“Even if you say Sisi doesn’t give freedom, where in the world is there total freedom?” said Ayman Fahri, 24, a Tunisian student in Cairo. He said he would take Mr. el-Sisi’s brand of effective authoritarianism over Tunisia’s turbulent fledgling democracy. “Look at Trump and what he did.”

Mr. Trump called the Canadian prime minister, Justin Trudeau, “dishonest and weak,” whereas North Korea’s brutal Mr. Kim was “funny.” He did not see the point of NATO but saluted a North Korean general.

He exited the Paris Agreement on climate change and the Iran nuclear agreement, and planned to leave the World Health Organization. He stood the postwar American-led order on its head. Even if the Biden administration moves fast to reverse some of these decisions, as it will, trust will take years to restore.

Mr. Ischinger said: “We will not be returning to the pre-Trump relationship.”

Dmitri Medvedev, the former president of Russia and now deputy head of Mr. Putin’s Kremlin Security Council, described America as mired “in a cold civil war” that makes it incapable of being a predictable partner. In an essay, he concluded that, “In the coming years, our relationship is likely to remain extremely cold.”

But the U.S. relationship with Russia, like other critical international relationships, will change under Mr. Biden, who has deep convictions about America’s critical international role in defending and extending freedom.

Mr. Biden has described Mr. Putin as a “K.G.B. thug.” He has pledged to hold Russia accountable for the August nerve-agent attack on the opposition leader Aleksei A. Navalny — an incident ignored by Mr. Trump in line with his uncritical embrace of Mr. Putin. Mr. Navalny was arrested this week on his return to Russia, a move condemned in a tweet by Jake Sullivan, the incoming national security adviser.

Mr. Putin waited more than a month to congratulate Mr. Biden on his victory. It also took a while, but souvenir stalls at Ismailovo, a sprawling outdoor market in Moscow, now stock wooden nesting dolls featuring Mr. Biden and have dropped Trump dolls. “Nobody wants him anymore,” said a man selling dolls. “He is finished.”

The world, like America, was traumatized by the Trump years. All the razor wire in Washington and the thousands of National Guard troops deployed to make sure a peaceful transfer of power takes place in the United States of America are testimony to that.

But the Constitution held. Battered institutions held. America held when troops were similarly deployed to protect state capitols during the civil rights movement in the 1960s. Mr. Trump is headed to Mar-a-Lago. And betting against America’s capacity for reinvention and revival was never a good idea, even at the worst of times.

Reporting was contributed by Vivian Yee and Nada Hussein from Cairo; Katrin Bennhold and Christopher F. Schuetze from Berlin; Ernesto Londoño from Rio de Janeiro; Catherine Porter from Toronto; Elisabetta Povoledo and Emma Bubola from Rome; Steven Erlanger and Monika Pronczuk from Brussels; Christina Anderson from Stockholm; Patrick Kingsley from Jerusalem; Steven Lee Myers from Seoul, South Korea; Farnaz Fassihi from New York; Benjamin Novak from Budapest; Ruth Maclean and Mady Camara from Dakar; and Andrew Higgins from Moscow.