Lebouf argues that the award should have gone to Portugal defender Pepe for his starring performances during the tournament.
The 25-year-old Griezmann scored six goals during his Euro campaign but could not find a way past Pepe and company during the final in which they lost 1-0.
"I like Griezmann a lot, but he was not the player of the tournament. I do not agree with this choice," Leboeuf said.
"We have to be critical. We only saw him from the quarter-finals on. He got two chances in the final, but he did not take them. We did not see too much of him otherwise.
"But UEFA has always worked like this. They always give man of the match to the player who scored, too.
"For me, there was someone like Pepe, you had Gareth Bale who led Wales the way. There were a number of players who showed a lot of quality.
"Pepe was in great form right from the start until the very end. Griezmann on the other hand was dropped for the second game."