In front of a capacity crowd in Budapest the world champions struggled to break down a tireless Hungary defence and, when they found a way through, were not clinical with their chances.
Benzema skewed wide after being teed up well by Mbappe, who headed wide from a good chance early on.
After a number of wasted chances, Hungary's Attila Fiola broke up the other end and stunned Les Blues with a well taken goal in added time at the end of the first half.
Antoine Greizmann levelled in the second half but the French, who will face Portugal in their final group game next week, could not find a winner.
"We should have been in front. It's not good enough given what we expected, but that's soccer," Deschamps said. "They scored with their only chance. Considering the context, we'll take the point.
"Hungary put on the match of their lives. Good for them."