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Pogba struggled to have an impact but Didier Deschamps' men still recorded a 4-1 victory over Bulgaria in World Cup qualifying.
Griezmann, who scored once and set up another, urged calm about the Manchester United signing's performance.
"Paul needs affection," he said, via L'Equipe. "He tries to do his best, give everything.
"He has a different game with [former club] Juve, Manchester and here."
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France fell behind to a Mihail Aleksandrov penalty in Paris, but a Kevin Gameiro brace and goals from Griezmann and Dimitri Payet saw them safely to victory.
Griezmann said all he wanted to see from Pogba was the 23-year-old contributing.
"We expect him to play for the team," he said. "Not that he scores goals from 50 metres."
France's win sees them sitting second in Group A of qualifying, level on points with Netherlands and Sweden.