PARIS – After a ceremonial weekend in France, President Donald Trump returned to the United States on Sunday to face an array of difficult political challenges – from decisions on the attorney general's job to ongoing investigations into him and his administration.

"Beautiful ceremony today in Paris commemorating the end of World War One," Trump tweeted during his last day in Paris, adding: "Now off to Suresnes American Cemetery to make speech in honor of our great heroes! Then back to the U.S.A."

Back in Washington, D.C., members of the incoming House Democratic majority served notice that they will vigorously investigate various aspects of his administration, including last week's appointment of acting Attorney General Matthew Whitaker.

Rep. Jerrold Nadler, D-N.Y., who will likely chair the House Judiciary Committee when Democrats take over in January, said Whitaker's past attacks on special counsel Robert Mueller suggest he might try to shut down the investigation into Russia interference in the 2016 election.

Saying he wants to summon Whitaker before his committee, Nadler told CNN's "State of the Union" that "the very first thing" he wants to do is "to protect the Mueller investigation."

More:Charles Schumer says Democrats might tie spending bill to Mueller protection

More:President Trump honors the dead of World War I – and avoids politics

Trump must also decide whether to appoint Whitaker full time to succeed fired Attorney General Jeff Sessions, or find someone new. Either way, the nomination of a new attorney general will likely generate difficult Senate confirmation hearings.

The Paris trip just days after Election Day, on which Democrats won control of the House while Republicans held onto the Senate.

As Trump landed Sunday back in Washington, he also faced other potential political headaches, Among them:

What is Mueller going to do?

Trump advisers like attorney Rudy Giuliani expect the special counsel to issue some kind of report soon on his findings in the Russia case. But no one knows for sure, especially with all the upheaval at the Justice Department.

Trump has denied any sort of collusion with Russians who sought to influence the 2016 campaign by hacking Democrats and pushing fake news. The president has repeatedly denounced the investigation as a hoax.

The hush money case

While Trump was in Paris, The Wall Street Journal reported that the U.S. attorney’s office in New York has gathered evidence of Trump’s participation in the pre-election payment of hush money to women who claimed to have had affairs with him.

The payments, designed to keep the women quiet, were not reported by the Trump campaign, and therefore could constitute violations of campaign finance laws. Trump has denied wrongdoing.

Nadler also expressed interest in whether Trump knew about hush money, telling CNN "that might very well be an impeachable offense."

How far to push on immigration

Before leaving Washington last week, Trump signed an order seeking to restrict asylum claims for migrants. It is being challenged in court.

Trump, who made attacks on caravans of Central American migrants a key part of his campaign for Republican congressional candidates, must now decide whether to act on other proposals he tossed out on the campaign trail.

That includes his call to end birthright citizenship. That kind of move would also be challenged in court.

What to do about Saudi Arabia

During his trip to Paris, Trump spoke with Turkish President Recep Tayyip Erdogan. Hours before, Erdogan had said he provided the United States and other countries with audio tapes demonstrating Saudi complicity in the murder of Washington Post journalist Jamal Khashoggi.

Trump must eventually say whether he believes the Saudis are guilty, and whether he will put sanctions on his Middle East ally.

The president also faces a number of other foreign policy challenges when he returns to the White House, including Iran, Syria, and North Korea.

Given his ceremonial obligations, Trump did little policy work in Paris, though he did have a one-on-one meeting with French President Emmanuel Macron.

Still, his foreign policy philosophy did come up during a ceremony to mark the 100th anniversary of the armistice that ended World War I.

Macron, who has criticized Trump's "America First" foreign policy, appeared to reference the U.S. president as he used his speech to decry excessive "nationalism" at the root of the First World War and succeeding conflicts.

"Nationalism is a betrayal of patriotism," Macron told a gathering of world leaders that ranged from Russian President Vladimir Putin to German Chancellor Angela Merkel, as well as Trump.

“Nationalism is a betrayal of patriotism by saying, ‘our interest first, who cares about the others?’"

Trump did not respond to Macron, at least publicly.

During his speech at the cemetery, Trump thanked Macron for inviting him to the armistice centennial.

"It was very beautiful and so well done," Trump said.