Translation:János sees large rivers next to the trees.
Because in your sentence, you have the prepositional phrase "next to big rivers", but Hungarian does not talk about anything being next to rivers.
Instead, it has the postpositional phrase a fák mellett "next to the trees".
Also, the thing that János sees is big rivers: they are marked with the accusative ending -(a)t as they are the direct object. Your sentence makes him see trees instead (and misses the definite article "the").
Janos sees big trees along the river. - János nagy fákat lát a folyó mentén. This sounds better to me as a native speaker:)