I think James had a normal relationship with his parents, just like everyone else has. Not too close, but not too far either.
They were barely mentioned in the books, only when Sirius said they were kind people and let him live with them when he escaped the Blacks. We don't even know their name.
When James and Lily were killed (

) they weren't alive, so I assume they were killed, too, in the war. Maybe they were killed because of the hunt for the prophecy, who knows.