Montpellier stunned France by winning Ligue 1 last season, pipping big-spending rivals Paris-Saint Germain to the title with Giroud starring in attack.
Papin believes that Rene Girard's side lack a consistent goal threat after selling Giroud to Arsenal during the close season.
He said: "When [Giroud] played, their teammates felt more secure.
"Other teams do not fear Montpellier anymore. They no longer fear that a guy will come along and change everything.
"The players change, but they are not pure goalscorers. They score from time to time, but not in every game [like Giroud]."
Montpellier currently sit bottom of Group B in their debut Champions League campaign and need a result against Olympiakos tonight to keep their slim qualification hopes alive.