The inauguration of Donald J. Trump is not just a restoration of power for the former president. It’s a return for his family, as well.

They left Washington four years ago, alienated from many of their former friends and acquaintances in New York City because of their work in the administration. They return to Washington with more political and cultural support — and a far better understanding of how to wield their soft power.

Of course, everyone is a little older. Barron Trump, who was in elementary school when Mr. Trump entered office in 2017, is now a college freshman at New York University. He towered behind Mr. Trump’s shoulder on Monday during the inauguration ceremony, seated next to his mother, Melania.

The incoming first lady was both visible and inscrutable, wearing a sharply tailored navy suit and a large boater hat that concealed her eyes. Mrs. Trump, who largely retreated from public view after leaving the White House, plans to join her husband in Washington, D.C., and participate in an Amazon documentary.

“This time, I have everything, I have the plans,” Mrs. Trump said in an interview on Fox News last week. “I already packed. I already selected the furniture that needs to go in. It’s a very different transition this time around.”

The family ties extend to Mr. Trump’s in-laws. Mr. Trump chose Charles Kushner, the father of his son-in-law Jared Kushner, to serve as the next U.S. ambassador to France. He named Massad Boulos, whose son is married to Mr. Trump’s daughter Tiffany, as a Middle East adviser.

Not everyone is more visible than they were four years ago. As Mr. Trump was sworn in, his four children — Donald Jr., Eric, Ivanka and Tiffany — gathered around him to celebrate his victory.

Donald Jr., who has emerged as a key conduit to his father’s base, appears poised to continue his role as the keeper of Mr. Trump’s political flame. Earlier this month, he traveled to Greenland in what appeared to be an effort to support his father’s threat to buy the nation.

Eric will continue his role running the family business, as executive vice president of the Trump Organization. His wife, Lara, recently stepped down as co-chair of the Republican National Convention.

Ivanka Trump and her husband, Jared Kushner, were key advisers during Mr. Trump’s first term, with offices in the West Wing. This time, the couple plans to remain in their lavish Miami mansion, where they retreated after Mr. Trump lost in 2020. Politics, Ivanka Trump said in a recent podcast interview, is a “very dark, negative business.”

The couple won’t escape the spotlight entirely. Mr. Kushner now runs a $3 billion private equity fund financed by the governments of Saudi Arabia, the United Arab Emirates and Qatar, as well as by Terry Gou, the Taiwanese billionaire and founder of Foxconn, the world’s largest contract electronics manufacturer. His ties are likely to prompt a steady stream of questions about whether the couple is getting special treatment from foreign governments, given their closeness to the president.

“Obviously the world is different for us over the next four years if her father is president,” Mr. Kushner said in October. “But, you know, either way, our life will just continue to move forward.”

Mainstream conservative lawmakers and politicians from Europe are planning to attend President-elect Donald J. Trump’s inauguration. But the European contingent is also expected to include leaders of some parties that are on the right-wing fringes in their own countries or have only recently begun to gain greater acceptance at home.

Many of the European politicians who have flocked to Washington share Mr. Trump’s anti-immigrant fervor.

Headlining the European attendees is Prime Minister Giorgia Meloni of Italy, according to her official agenda. Ms. Meloni, a conservative, was one of the first leaders to visit Mr. Trump at Mar-a-Lago after his election, on Jan. 4.

Ms. Meloni, who is trying to stop the flows of migrants to her country, is considered one of Europe’s strongest leaders, and her supporters hope that she will emerge as a privileged ally of Mr. Trump in Europe.

The most notable absence is Prime Minister Viktor Orban of Hungary, one of Mr. Trump’s most fervent fans in Europe. Despite being widely admired by many American conservatives as an ideological beacon and praised by Mr. Trump as “fantastic,” Hungary’s proudly illiberal leader was not invited to attend, according to a Facebook post by Zoltan Kovacs, Hungary’s secretary of state for international communications.

“To be crystal clear: Viktor Orbán will not participate in the event. President Trump’s team — in accordance with tradition — did not invite any foreign heads of state or government,” Mr. Kovacs said.

That is clearly not true. Mr. Trump has made a point of breaking with tradition and inviting foreign leaders to attend, including Xi Jinping of China. (Mr. Xi is sending the country’s vice-president.)

Here are some of the Europeans who plan to make an appearance

Éric Zemmour, who has been convicted in France of inciting racial hatred, has announced he was invited to attend the inauguration. Mr. Zemmour has written best sellers denouncing the supposed decline of a nation whose Christian roots were being undermined by Muslim immigrants and their descendants.

The former television pundit, whose 2022 run for the French presidency was inspired by Mr. Trump’s campaign, wrote on X, “The wind of freedom blowing through the United States will soon be blowing through France.”

Mr. Zemmour won only 7 percent of the vote in the 2022 presidential election, and his party has only one lawmaker at the E.U. level — Sarah Knafo, Mr. Zemmour’s partner, who is planning to attend the inauguration with him.

France’s much more powerful nationalist, anti-immigrant party, the National Rally, said it was sending a delegation, but neither Marine Le Pen, the party’s longtime leader, nor Jordan Bardella, its current president, will attend.

While Mr. Trump’s anti-immigrant message resonates with the National Rally, which is considered far-right in France, his wrecking-ball approach to politics runs counter to the party’s yearslong, and increasingly successful, efforts to shed a more extreme image.

Mr. Bardella told CNews television last week that he did not understand the “fad” of racing “to get your picture taken in front of Donald Trump during his inauguration speech.”

The contingent of Germans planning to attend the event includes a representative from the mainstream conservative party — Jürgen Hardt of the CDU/CSU, which leads in the polls for Germany’s coming election. But a member of the Alternative for Germany, or AfD, parts of which are classified as right-extremist by the German government, is also expected to be there.

The AfD representative will be Tino Chrupalla, its co-leader, rather than Alice Weidel, its chancellor candidate in the February election. Elon Musk, Mr. Trump’s billionaire ally, recently hosted a friendly interview with Ms. Weidel on his X social network, giving the AfD a platform that German media and politicians have long denied it. Mr. Musk has endorsed Ms. Weidel in the election.

Among the expected high-profile British guests are former Prime Minister Liz Truss, who resigned after less than two months in office over a budget plan that rattled financial markets, and Nigel Farage, who leads the country’s insurgent, populist and anti-immigrant party, Reform U.K.

Mr. Farage is a longtime ally of the president-elect, and backed his campaigns for the White House in 2016 and 2020 as well as last year.

While in Washington, Mr. Farage may have the chance to try to repair his ties with Mr. Musk, who had been a supporter but recently turned on Mr. Farage. The spat started over Mr. Farage’s refusal to echo Mr. Musk’s demand that a far-right agitator with multiple criminal convictions be released from prison.