Former Chelsea winger Keenan, 26, joins after a spell with Melbourne Victory, while Thicot, 21, - who can play in defence or midfield - was released by Nantes last month.
"Joe has done well on trial and Steven shows fantastic maturity."
Paatelainen said he was confident both players would be good additions to his squad at Easter Road.
"Steven is a young player who shows a great deal of maturity and a fantastic approach to the game, he is a very good player who can play in a number of positions and has come through all the French national teams alongside some of the top players in the world," said the Hibs boss.
"He has plenty of ability and like Joe is a very ambitious footballer, which is something I like to see."
