Even if one accepts that there really is such a thing as unconditional love between humans, it’s notable by its absence from the relationship between Helen and Paris. To a large extent, this is because they only got together due to the devious machinations of the gods. Paris was awarded Helen as a prize for choosing Aphrodite as the fairest goddess of them all.
Unfortunately, Helen was already married—to King Menelaus of Sparta, no less. Paris’ appropriation of her constituted an act of war, and so the long, epic conflict of the Trojan War got underway. Essentially, Paris was bewitched by Helen’s remarkable beauty and subsequently took leave of his senses. Any love that he and Helen may have shared was entirely conditional, based as it was on the chicanery of the gods.
As the relationship wasn’t founded on love, it comes as no surprise to find that, as the war rages outside the walls of Troy, Paris and Helen don’t seem to have much time for each other. Paris is berated by Hector for not strapping on his armor and entering the field of battle to fight. Paris’ cowardice indicates that he doesn’t really have very powerful feelings towards Helen. If he did, then at the very least, he would fight for her honor.
As for Helen, it’s evident that she has very little emotional connection to Paris, despite everything that’s happened. Even with Paris around, she feels alone and empty. After Paris finally puts on his armor and heads off to battle, she also starts pining for her husband, her homeland, and her children. Under the circumstances, Helen’s extraordinary beauty has availed her absolutely nothing and has brought nothing but death, destruction, and bloodshed in its wake.