Attila Fiola had given the host a dreamy halftime lead after France missed a slew of early chances.
But Greizmann equalized in the 66th minute to take France to four points as Hungary kept their hopes low, on one point, in a group where they had had little luck with heavyweights Germany and Portugal as well. in the mix.
READ: UEFA Euro 2020 Hungary vs France Highlights
A crowd of 65,000 people, mostly Hungarian, who have not been seen in football since the start of the COVID-19 pandemic, wanted to share the points under the summer sun even though they were largely dominated.
Greizmann finished with a powerful shot but at the end of an unusual move from the French, who for all their cunning and panache in midfield needed a Route One kick from their goalkeeper to shape their equalizer.
France had three exceptional chances in the first half that their much-vaunted attack should have ended.
READ: EURO 2020: Points table, goals scored, goal difference
Peter Gulasci made a double save from Karim Benzema and Griezmann in the first quarter of an hour, then watched with relief as Kylian Mbappe walked up a few yards after Benzema pushed him in the 17th minute.
It seemed like a matter of time before the Blues broke the deadlock, but when Mbappe returned the favor to Benzema just past the half hour mark, he managed to hit a disappointing shot as it seemed easier to to mark.
France’s lavishness was then punished at the end of the half as winger Fiola recovered a cross pass from Adam Nagy, played a one-two with Roland Sallai and passed the French defense to return coldly at home. of the ecstatic crowd.
Until then, there had been hardly any Hungary, losing skipper Adam Szalai to injury in the first half.
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It was not until the 66th minute to equalize. Goalkeeper Hugo Lloris hit the ball in the center of his penalty area, which the Hungarian defense allowed to bounce back for Mbappe to reach first with his frightening pace. His square ball was barely intercepted by Willi Orban, whose efforts to clear only succeeded in giving Griezmann a hit.
Hungary will face Germany on Wednesday in Munich while Portugal and France play in Budapest at the same time.