Cameroon’s Communications Minister Issa Tchiroma Bakary told the BBC the Moulin-Fournier family, including four children, were in good condition.
In a video published on YouTube, militants from the Nigerian group Boko Haram had claimed to be holding them.
The French president said France had not paid a ransom to free the family who are now in the capital, Yaounde.
The family arrived at the French embassy with a heavy security escort, the AFP news agency reports.
President Francois Hollande said secret talks had been taking place for the past few weeks to help secure their release, Reuters news agency reports.
“France has not changed its position, which is not to pay ransoms,” the agency quotes him as saying at a news conference in Paris.
“I spoke to the father this morning… He told me how happy and relieved he was.”
The release of the hostages was announced on national radio in Cameroon on Friday morning.
The statement from the presidency said they had been handed over to Cameroon authorities late on Thursday.
Both the Nigerian and French governments were thanked in the statement, but no further explanation was given about how they were freed.
The French president’s office said that Foreign Minister Laurent Fabius had immediately left for Cameroon to greet the family, AFP reported.
Mr Fabius told AFP the French hostages were freed overnight “in an area between Nigeria and Cameroon” and would be flown to France on Saturday.