While the circumstances of the priest's release are unclear, Fabius insisted that France, often accused of paying ransoms for hostages despite stiff government denials, had not paid for the release of the priest.
"The French government does not pay ransoms. There were discussions," Fabius told journalists.
The banned Nigerian Islamist group Boko Haram on Wednesday said it had released a French Roman Catholic priest on compassionate grounds but insisted that no ransom had been paid.
A source within the group said they had demanded a ransom from France through the Cameroon government to release the 42-year-old, who was freed on Tuesday and arrived back in France on Wednesday.
But the French government had refused and requested that Vandenbeusch be released on humanitarian grounds because of his status as a clergyman, the
"The leadership [of Boko Haram] decided to release the priest on compassionate grounds and having benefited from his medical expertise," the source told the French news agency AFP.
"The priest offered medical service to sick members during his period of captivity. The leadership felt there was no longer need for keeping him."
In his former parish of Sceaux, near Paris, bells rang on Tuesday to celebrate his release.
In a statement, his family thanked French, Cameroonian and Nigerian authorities and all those who supported them during the ordeal.
"At this time of joy, we do not forget the other French hostages, and are thinking of their families," they said.
There are still six French people being held hostage in Mali and Syria, and Hollande also reiterated his support for their families.