But his health care bill didn't come up for a vote in the House, his travel ban was twice blocked in the courts and his West Wing has been plagued by infighting and the resignation of his first national security adviser amid an ongoing investigation into contacts between Trump aides and Russian officials.
The terrorist group said it was behind the attack and named the gunman as Abu Yusuf al Beljiki, suggesting he was from Belgium.
Speaking at a news conference in Paris, Molins said Cheurfi aged 39 had been identified by documents found in the auto used in the attack.
Police tape surrounded the quiet, middle-class neighborhood and anxious neighbors expressed surprise at the searches. He spent 11 years in jail after shooting two police officers in 2001.
A second suspect who might have been involved in the incident on the Champs Elysees shopping boulevard may still be on the loose, authorities said. He also said the U.S.is committed to a strong Europe, but he didn't say directly whether he prefers that the European Union stay intact.
Mr Molins did confirm a note found near Cheurfi's body after he was shot by police had handwritten messages defending IS and the addresses of security sites. Belgian authorities said they had no information about the suspect.
Describing the Champs Elysees shooting as an attack on democracy, he urged voters: "Do not give in to fear".
A man got out of a auto and targeted the police directly, Ministry spokesman Pierre Henry Brandet said, adding the driver was believed to be on the loose.
Brandet said officers were "deliberately" targeted, as has happened repeatedly to French security forces in recent years, including in the run-up to the 2012 election.
The touristic area has been evacuated and closed off. Subway stations were closed off.
A Hawke's Bay couple were enjoying their honeymoon on the most famous boulevard in the French Capital when gunfire erupted and sent scores of tourists fleeing into side streets. "Some were crying. There were tens, maybe even hundreds of them".
"Another terrorist attack in Paris", Trump said on Twitter on Friday morning. Hollande, who's not seeking re-election, convened a meeting of the national defense council on Friday. French Interior Minister Bernard Cazeneuve said on April 21 that the elections would not be suspended because of the attack.
One of the key questions was whether, and how, the attack that killed one police officer and wounded three other people might impact voting intentions.
The attack brought back the recurrent campaign theme of France's fight against Islamic extremism, one of the mainstays of the anti-immigration platform of far-right leader Marine Le Pen and also, to a lesser extent, of Fillon. She canceled a minor campaign stop, but scheduled another.
Centrist candidate Emmanuel Macron appealed to French voters to keep a cool head.
Socialist Benoit Hamon tweeted his "full support" to police against terrorism. The two top candidates will qualify for the runoff election on May 7, and at this point any combination among the four leading candidates appears possible.