France dominated both halves, enjoyed more possession, more attempts and more attacks but ultimately, they came up short against an ambitious Hungarian side.
The hosts opened the scoring moments before the half-time whistle.
Attila Fiola was the man who made the breakthrough after beating Hugo Lloris from close range. The near-full Puskas Arena erupted as the Hungarians threatened to pick up their first win over France since 1971.
That was not to be as Didier Deschamps' side came out firing in the second-half and scored the equaliser in the 66th minute.
Antoine Griezmann was the goalscorer as France breathed a huge sigh of relief.
Despite piling on the pressure in the latter stages, the visitors were unable to find the winner.
Instead, it was Hungary who celebrated a memorable draw against a formidable opponent.
You can read the full match report on our sister site, Football365.
Stat of the day
From OptaJoe: Antoine Griezmann's equaliser for France was his seventh goal at the European Championships; only Cristiano Ronaldo (11) and Michel Platini (9) have scored more in the competition's history.
The group of death just keeps on giving with France set to take on Portugal on Wednesday night.
The defending World champions against the defending European champions - this has the makings of an absolute classic.
Hungary, on the other hand, will have to prepare for another formidable opponent.
After the challenge of Portugal and France, Marco Rossi's men will travel to the Allianz Arena to take on Germany.