Alain Goma dropped anchor in Hodeida on June 3 after running out of water while sailing to India.
Hodeida is under the control of Iranian-backed Huthi rebels, who took him prisoner.
It is not clear whether they made any demands of France in return for the release of Goma, who is in his fifties.
In a statement President Emmanuel Macron thanked authorities in Oman and Saudi Arabia for helping obtain his release.
He described Oman's role as "decisive" but said Saudi Arabia had also provided "assistance."
Goma's release comes as Saudi Arabia battles allegations that officials murdered a US-based Saudi journalist, Jamal Khashoggi, at the Saudi consulate in Istanbul.
Khashoggi was critical of some of the policies of Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman.