"I just filed an appeal" with the Tizi Ouzou Court, said lawyer Salah Brahimi, referring to the city where the journalist has been imprisoned since being convicted on Sunday.
Gleizes, 36, who specialises in African football and contributes to So Foot magazine, travelled to Tizi Ouzou to write about the local football club Jeunesse Sportive de Kabylie, named after Algeria's Kabylia region, home to the Amazigh Kabyle people.
He was arrested in May 2024 and then placed under judicial control and prevented from leaving the country, according to Reporters Without Borders.
It said Gleizes had in 2015 and 2017 been in touch with a Tizi Ouzou football figure prominent in the Movement for the Self-Determination of Kabylie (MAK), designated a terrorist organisation by the Algerian authorities in 2021.
Algerian authorities sentenced him on Sunday to seven years in prison for "glorifying terrorism" and "possessing publications for propaganda purposes harmful to national interests", the media rights campaigners said.
His lawyer said he expects the appeal case to be heard in October at the earliest.
The jailing of Gleizes comes at a time of growing tension between Algeria and its former colonial power France.
Algeria arrested and jailed French-Algerian writer Boualem Sansal in November on national security charges and has defied calls from President Emmanuel Macron for his release.