Dembele won the Ballon d'Or on Monday after a stellar year with PSG.
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Former France teammate Giroud told L'Equipe: "Did I see Ballon d'Or potential in him? It's hard to say.
"When I saw him every day for the French national team, no, I didn't necessarily say to myself, 'He's a potential Ballon d'Or winner.'
"To win a Ballon d'Or, you need talent but also a good season that catapults you to the forefront.
"He has the talent, but he needed to have the right season, with the right club, and win everything like he did, because the Ballon d'Or always depends largely on the team."