The 21 year old is a free agent after he was released by his former club Nantes at the end of last season.
Paatelainen feels Thicot has promise, and has revealed talks are under way over bringing the versatile midfielder to Easter Road.
"He is a good player, he can play various roles and we are now working hard towards a contract. Hopefully, he will join us," Paatelainen told the Scotsman.
"Steven has been through all the national teams in France, he's played with all the top names. He has plenty of ability and he tells me he is a very ambitious player which I like."