The late-night attack on the capital's famous Champs Elysees Avenue, which also left two officers wounded, made security a pressing issue ahead of Sunday's first round of voting in the presidential election.
A high-level meeting was held on Friday to review the country's security measures for the day. He was the subject of a "Fiche S" surveillance file and was on the radar of the French domestic security service DGSI, the source said.
The murdered police officer has been named as Xavier Jugelé and was said to be just days from celebrating his 38th birthday.
In addition to the assault rifle used in the attack, a pump action shotgun and knives were in his vehicle, the police sources said.
France takes to the polls on Sunday in the first round of a closely fought presidential election.
With a record number of voters still undecided, analysts say the shooting could play into the narrative pushed by the far-right.
Two of the main candidates, conservative Francois Fillon and centrist Emmanuel Macron, cancelled planned campaign stops on Friday.
Mr Trump tweeted hours after a gunman shot dead a policeman and wounded two others on the world-famous Champs Elysees boulevard.
Left-wing insurgent Jean-Luc Mélenchon warned against allowing panic to "interrupt democracy".
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The 48-year-old National Front leader called for France to "immediately" take back control of its borders from the European Union and deport all foreigners on a terror watch list.
"I was here working on the Champs-Elysees", he said. He fired twice, seriously wounding both men in the chest.
The offices of Charlie Hebdo magazine were hit in January 2015, IS gunmen and suicide bombers killed 130 people in Paris the following November, and a Tunisian man rammed a truck through crowds in Nice last July, killing 86 people.
Paris Prosecutor François Molins on Friday said Cheurfi had shown no signs of "radicalization". The French security official said Cheurfi had not been identified as a potential threat to national security, but did have a previous conviction for violence against the police and a history of radicalization.
She criticised outgoing Socialist President Francois Hollande as "notoriously feeble" and said France was "worn out by inaction". Cheurfi shot the officer and the officer's brother after crashing into a ditch.
Two radicalised men were arrested in the southern city of Marseille on Tuesday and authorities believe they had been trying to launch an "imminent" attack on the campaign.
In Washington, President Trump said the shooting in Paris "looks like another terrorist attack".
"We shall be of the utmost vigilance, especially in relation to the election", he told the nation on television. "And what can you say - it never ends", he added. "The Prime Minister has tonight passed on her condolences to President Hollande".
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