Interior Minister Gérald Darmanin said France had deployed unprecedented resources to capture the armed gang, including assistance from foreign countries. Four-hundred and fifty officers were deployed to Eure region where the attack took place.
"We are investing considerable resources, we are making a lot of progress," he told RTL radio on Wednesday.
Across France, thousands of prison guards staged a symbolic 24-hour shutdown of jails in support of their slain colleagues.
Right-wing politicians said the brazenness of the assault showed that the centrist government had lost its grip on drug crime, comparing France to countries with longstanding reputations for endemic gang violence.
"We're on a path to Mexicanisation," Bruno Retailleau, leader of the main centre-right opposition party in the French senate, said in a radio interview. "Prisons are sieves. Dealers run their drug trafficking businesses from jail."
Far-right politician Marion Marechal posted a video on X of herself offering support to guards outside a prison in Bordeaux.
"We have the impression of being in a third world country," she said, after one of the guards asked how such a violent attack could take place in France.
Known as "The Fly", fugitive Mohamed Amra is a 30-year-old from northern France, according to the Paris prosecutor's office. Police sources said he was involved in drug trafficking.
The Paris prosecutor's office said he had been convicted of burglary by a court in Evreux on May 10 and was being held at the Val de Reuil prison. He had also been indicted by prosecutors in Marseille for a kidnapping that led to a death, it said.
Tuesday's attack came on the same day that France's Senate released a major report on drug trafficking, warning that the country faced a "tipping point" from rising violence.
The report recommended the creation of a French version of the US Drug Enforcement Administration to combat a powerful national drug trade with annual turnover of 3.5 billion euros ($A5.7 billion).
