Jeremy Sidney, 33, was gunned down as armed officers swarmed into his house in Strasbourg, France.
He was a French national who spent time in prison for drug-taking and had only recently converted to Islam, the Sunday Express reported.
Seven others, including another gunman in Paris, were arrested during an anti-terrorist operation in the French capital, as well as Strasbourg, Cannes and Nice.
All were suspected of being involved in an attack on a Jewish shop in Paris last month in which one person was injured.
Sidney's fingerprints and DNA were said to have been found on an explosive device used, according to the newspaper.
President Francois Hollande stressed "the full determination of the state to protect French people against all forms of terrorist threats".
The eight men were said to be linked to a Salafist group which is committed to waging a jihad, or holy war, in Europe, the Express added.
London: A suspected Muslim terrorist in France has been shot dead by police in front of his pregnant wife and child, a media report said Sunday.
First Published: Monday, October 08, 2012, 00:22