"I saw him crossing" vs. "I saw him cross" [duplicate]
They are both correct, grammatically speaking. However, they have slightly different meanings.
I saw him crossing the road.
... suggests that you saw a male person in the middle of crossing the road (he was probably walking in the middle of the road toward one of the sides). But, you didn't necessarily see him get to the side of the road
I saw him cross the road.
... suggests that you saw him do the entire action of starting on one side, walking across, and ending up on the other side.