In the movie John Carter, he (John Carter) is able to jump high because of low gravity but how does he survive there if the atmosphere is so different than Earth's?
The movie John Carter, is based on the Barsoom novels by Edgar Rice Burroughs - in particular A Princess of Mars.
Burroughs began working on the novel in 1911 and at that time, current scientific theories about Mars were very different from what we know today. Wikipedia gives credit for much of the scientific background to the book Mars by the astronomer Percival Lowell (published in 1895). In all likelihood there were other inspirations such as Camille Flammarion, whose Wikipedia entry says that Burroughs "are referring to him in their writing", and Giovanni Sciaparelli, whose Wikipedia article describes the origin of the idea for canals on Mars:
During the planet's "Great Opposition" of 1877, he observed a dense network of linear structures on the surface of Mars which he called "canali" in Italian, meaning "channels" but the term was mistranslated into English as "canals."