The 26-year-old, identified as Romain, was detained in September last year in the Normandy department of Calvados, where he lives.
Prosecutors say he acted as administrator of the Ansar al Haqq website, a "reference" for the radical Islamist movement, and as a translator of "Inspire" magazine, which is put out by militant group Al-Qaeda in the Arabian Peninsula (AQAP), Paris prosecutors said.
His arrest was the first made under a new law passed in the aftermath of the Toulouse shootings, carried out by self-proclaimed Al-Qaeda inspired gunman Mohamed Merah. The government reacted to the shocking killings by making incitement to terrorism an offence punishable by five years in prison and a fine of up to €45,000 ($61,800).
Romain converted to Islam when he was 20, prosecutors said. At an earlier hearing he apologized for his actions, saying "I am sorry, I take responsibility".
"I did not intend to break the law or incite people to do wrong," he said.
At his trial on Tuesday he said: "I had no intention of encouraging people to attack France or the United States. I regret it and if I could go back I would not have done it."
The Ansar al Haqq website that he manages "has more than 4,000 members including 685 that are active" and Romain published statements from Al-Qaeda's north African branch AQIM on it, they added.
They said an investigation also found that the suspect had "an active role in the translation into French and the distribution of the tenth and 11th editions of the magazine Inspire."
Inspire is an English-language propaganda magazine published by AQAP that offers theological support and praise for jihadists.
Romain's lawyer Thomas Klotz saidthat the charges were against the European Convention on Human Rights and that his client was the only person in France being held under the new law.
Nevertheless judges were not convinced by the defense and handed Romain a one-year jail sentence.