It is hoped that a transfer will be pushed through before Wednesday return from their pre-season training camp in Slovenia.
An undisclosed fee has been agreed for the 22-year-old with his current employers Istres.
He is under contract in his homeland until 2016, but relegation out of the French second tier has forced Istres into a sale.
Tardieu is having to be patient, though, as Wednesday are waiting on Football League ratification of their takeover by Azerbaijani businessman Hafiz Mammadov.
Once that has gone through, Gray will be in a position to add fresh faces to his ranks at Hillsborough.
He said in The Star: “Florian is a creative midfielder.
“He has a good range of passing with both feet. He can pass it short or go long and he’s got a good engine.
“Hopefully we can get it sorted before we come back from Slovenia.”