Interior Minister Claude Gueant said the suspect, Mohamed Merah, was killed after he opened fire at police and jumped through a window during a police raid on his apartment on March 22 in the city of Toulouse.
French prosecutor Francois Molins told journalists Merah was shot in the head during the shoot-out.
Two French police were reported injured in the raid.
Molins also said Merah had videotaped all three of his attacks and confirmed that police have recovered the footage. Molins said that during the 32-hour standoff with police, Merah claimed that he had posted the video to the Internet.
However, authorities were not able to confirm that claim.
Merah, a 23-year-old French citizen of Algerian descent, had allegedly linked himself to the Al-Qaeda terrorist network.
Police said he told officers he was responsible for the murders of three French soldiers, a rabbi, and three Jewish schoolchildren in three separate shootings this month.
Merah reportedly said he was proud of the killings and that he had planned more attacks.
In a brief statement following the raid, President Nicolas Sarkozy congratulated police on the operation and cited efforts to capture Merah alive.
"Everything was done so that the killer would be handed over to justice," he said. "But endangering lives to achieve this objective was inconceivable. There have already been too many deaths."
Sarkozy, who is seeking reelection in presidential polls due to start in April, warned that because of the case the French government will in the future seek to crack down on what he described as "anyone who regularly visits websites which support terrorism or call for hate or violence."
It was not immediately clear which websites would fall under this definition.
Call For Calm
Sarkozy also called for social unity despite widespread anger over the killings.
"Today, the French must overcome their indignation and refrain from anger," he said. Our Muslim compatriots have nothing to do with the crazed motivations of a terrorist."
French intelligence officials are already coming under fire for not dealing with the threat posed by Merah earlier.
Reports suggest Merah had at least 15 previous criminal convictions -- some for violent acts -- and it was known that he had visited Afghanistan and Pakistan.
Both Merah and his brother had been registered in France as followers of the radical Salafist ideology.
Interior Minister Gueant defended the work of the government, saying some 700 suspected Islamic militants had been detained over the past decade and about 60 "Islamists with terrorist tendencies" have been imprisoned in France.
There had not been an Islamist terrorist attack on the French mainland since 1996.