Attila Fiola put Hungary ahead at the end of the first half and left France to scramble for a goal.
France coach Didier Deschamps will be frustrated with the result as France seek to exit Group F – the competition’s toughest group – ahead of Portugal and Germany who will play later on Saturday.
– Euro 2020 on ESPN: Stream LIVE matches and replays (US only)
– Calendar and calendar of Euro 2020 meetings
France dominated possession with 70 percent of the ball in the first half but missed several opportunities to take the lead.
Kylian Mbappe, Karim Benzema and Griezmann all missed their first chances to secure a lead and they must have regretted those opportunities when Fiola put Hungary ahead at half-time.
In a moment of brilliant individual skill, Fiola received the ball from Adam Nagy and headed for Hugo Lloris’ goal. He received the ball from Roland Sallai and reeled his shot into the net, to the delight of the 67,000 local spectators.
Hungary came out with more confidence in the second half but made an unfortunate defensive error to allow France to return to the game in the 66th minute.
Lloris threw a long ball into the field which the Hungarian endline allowed to bounce back, giving Mbappe time to run over it. He placed a cross into the box that Willi Orban hit directly in the path of Griezmann – who was making his 50th consecutive start for France – who hit him in the net.
Mbappe was fortunate enough to put France 2-1 moments later, but snatched his shot right off the post.
Hungary will face Germany on Wednesday in Munich while Portugal and France play in Budapest at the same time.