"He's played Champions League football and been in and around the top of the French league with Marseille," Allardyce told reporters.
"I spoke to [former West Brom manager] Steve Clarke about the player. He's a creator with a few goals to add to that, and if we can get a few more goals out of him that would be fine. Last season goals were a struggle, not the performances, that's why at times we didn't win as many games as we should have.
"He's a creative player and can play in a number of positions. For him to get better than four goals, that would be a great addition to our overall total. Him and Alex Song were two exceptionally good signings late in the transfer window."
Amalfitano won his sole cap for the French national side in 2012.