Also in Group A, Belarus rallied to top Kazakhstan 5-2.
The Czechs went up 5-0 when Lukas Kaspar scored six minutes into the third period, before France pulled two goals back in two minutes through Yorick Treille and Laurent Meunier.
Jagr then set up Miroslav Blatak for a power-play goal with 33 seconds left for the final score.
Also in Group C, Matt Weinhandl had three goals in Sweden's 5-2 win over Norway.
The Associated Press contributed to this story.