Ibn Yacoub was "exhausted after two months incarceration" but happy, BarakaCity said in a Tweet that reported that he had talked to its president by telephone from Bangladesh.
But he cannot leave the country, it added, and the charges against him still stand.
The 28-year-old was arrested because the Muslim name he uses is not the same as the one on his identity papers and passport, Puemo Maxime Tchantchuing.
He is also accused of failing to notify the authorities of his presence and work.
BarakaCity argues that this was impossible because he was working with Rohingyas, Muslims from Myanmar regarded as illegal immigrants by Bangladesh.
Although the case initially attracted less media coverage than other cases of French citizens arrested abroad, an online petition has collected 430,000 signatures since Christmas, his portrait has been exhibited in front of the council offices in Montreuil on the Paris outskirts and Socialist MP Benoît Hamon took up his case with Foreign Affairs Minister Jean-Marc Ayrault on Tuesday.
BarakaCity, whose leaders describe themselves as "orthodox" Muslims, attracts support from many young Muslims but has also excited controversy.
Its founder, Idriss Sihamedi, was criticised for limiting his criticism of the Islamic State armed group to a condemnation of "all atrocities committed by armed groups, government and juntas" during a television appearance where he was pleading Moussa Ibn Yacoub's case.