Paladins' powers come from the oaths that they swear or the Gods that they follow (depending on edition). If they break their code, according to you, the DM, you have every right to disallow them from using their powers.

You could either tell him upfront: "You no longer feel the blessing of Torm with you. Your swings feel weaker and you cannot channel his divine magic like you could before."

Or you could let him figure it out: "You use your lay on hands, but feel no healing energy enter your body," or "You swing your sword at the hobgoblin. It connects, but you no longer feel the divine fury you used to wield being channelled through the blade. There is simply a dull, mundane, slicing sound."

If the player doesn't want that to happen, you could consider allowing him to redeem himself. As a DM, I only ever allow redemption through sacrifice (though I've never told my players this directly). Basically, he's going to have to give up either max HP, a valuable ability score (str, con, wis, cha), or something even more precious, through some event.

Examples of Redemption Quests I've done before -- a Paladin failed three Wis saves in a row attempting to restrain himself, and brutally murdered an unarmed prisoner who was taunting him about his dead family. The quest involved him having to hunt a child who had been possessed by an evil spirit. The child's body was frail, so much so that any attempt to physically restrain it risked serious harm. The Paladin had to distract the spirit/child while the rest of the party completed the exorcism ritual. He had to sit there and let the spirit torture and torment him without fighting back as a distraction. He ended up losing 2 str and 2 wis permanently, as a result of the physical and psychological scarring.

Another Paladin let a bandit leader escape because he wanted to grab the bandits' treasure horde. He got a lot of coin, but the bandit leader took vengeance on the family that ratted him out, killing them all. The Paladin tracked down the bandit leader, who had taken the family's youngest son with him as a hostage. The Paladin, through some good rolls and good RP, convinced the leader to take him hostage instead of the boy, knowing that the bandit leader wasn't going to be able to get away alive. With the boy safe, the rest of the party charged. The bandit slit the Paladin's throat and threw him off a ledge. He failed his death saves before the party could get to him.