No, the Paladin would not immediately know if the Rogue failed or not.
Antimagic Field states (Emphasis mine):
Any active spell or other magical effect on a creature or an object in the Sphere is suppressed while the creature or object is in it.
The ability to sense whether or not someone resisted the Zone of Truth is itself a magical effect of Zone of Truth for the paladin. Being in the Antimagic Field would suppress that effect.
The knowledge is lost, but the Paladin may still be able to deduce if they were affected or not after stepping out of the Antimagic Field.
@BenBarden pointed out that since the knowledge only happens when they make the saving throw, the knowledge is lost. If the Zone of Truth has ended, the Paladin will never know. However, per this question and accepted answer, if the spell is still ongoing and the Rogue succeeded in their saving throw, they will continue making saving throws, so the Paladin would be able to tell after they step out of the Antimagic Field. And, if they had already failed, they will stop making saving throws. So the Paladin can assume
- If they are getting new information from Zone of Truth, the Rogue had resisted the effects while the Paladin was in the Antimagic Field
- If they get no new information, the Rogue had failed to resist, and must tell the truth
Again, though, the Paladin would need to step out of the Antimagic Field to be able to tell anything at all.