A combination of poor form, injury and illness has meant Pogba has started only four of United's last 11 matches in all competitions, while speculation has persisted over a rumoured breakdown in his relationship with manager Jose Mourinho.
France boss Didier Deschamps conceded this week that the 25-year-old "can't be happy" with the way life is going at Old Trafford.
"He came back [to the squad] with a huge smile on his face," Griezmann told a news conference. "He was happy. It's not easy when you don't play at your club or you don't feel at your best. It happened to me and he knows that.
"He still enjoys having fun and working hard, which are what matter the most. It's up to him to prove and show that he's still the player that he can be.
"The coach trusts him, like the entire squad. We need a smiling Paul and an efficient one on the pitch."
Griezmann's own future has again come under scrutiny this week, with the Atletico Madrid star telling L'Equipe he does not want to head into the World Cup without knowing where he will be playing his club football next season.
Barcelona have been heavily linked with a move for the forward but he says it is not certain he will leave Atletico at the end of 2017-18.
"My future will be decided before the World Cup. A while before it," he said. "I said the same to my club and my sister. There are no worries about it.
"I had a complicated start to the season but I am feeling well in Madrid and we are going forward with the club.
"I want to win a title. I think that I can with Atletico. I still have a lot to learn from the coach."