Lock Maestri has agreed a four-year contract with Stade, while centre Fickou is tied to the club until the end of the 2022-2023 season.The duo have been named in Jacques Brunel's France squad for the tour to New Zealand in June.
"We are very proud of these signings. Yoann is a worker, he is a player who will bring all his experience of major events," Stade president Hubert Patricot said. "Gael is young but he also has international experience. He will continue to grow with our project and will be able to display all his talent with us.
"Both are totally committed to the philosophy of play we want to develop here and the ambition [chairman] Hans-Peter Wild has for Stade Francais."
Maestri has made 59 appearances for Les Bleus, while Fickou has featured in 35 Tests.
Stade earlier revealed former South Africa international Morne Steyn agreed a one-year contract extension with an option for a further year.
The Top 14 club narrowly avoided a relegation play-off and only finished six points clear of bottom side Brive.