Gouffran became part of a burgeoning French revolution at St James' Park on Tuesday, signing a four-and-a-half year deal after a fee was agreed with Bordeaux for his services.
Newcastle sit just two points ahead of the bottom three but Gouffran thinks his arrival plus those of compatriots Mathieu Debuchy, Mapou Yanga-Mbiwa and Massadio Haidara will soon remedy their run of bad form.
"I am not worried at all," Gouffran said. "I know the players who play here at Newcastle already. They are fantastic players.
"Newcastle isn't in the position it should be in the league. Whether it's myself or the other players in the team, we are going to try our utmost to make sure we can climb up the league to where we should be.
"I think with the players Newcastle have, we can realistically be aiming to finish at least in the top eight."
Gouffran, who says pace is one of his main attributes, also believes it is unfair to tab him as a direct replacement for Demba Ba, who left for Chelsea earlier this month.
He added: "There's not really any added pressure. Yes, I am an attacker, yes, I want to score goals, but we both have different styles of play. I don't really think it's fair to draw any comparisons between both of us. Each player has his own style. Each to his own.
"Papiss Cisse and I played against each other when he was at Metz in France and he is someone who has really made a lot of progress here at Newcastle and he has scored some great goals.
"I had a chat with him this morning for the first time. We get on really well. He's a great guy and I have no worries that we can definitely play together well."