It seems to me that
Han only approached Kylo Ren because Leia specifically asked him to bring their son back. And he seemed a bit hesitant to do it.
Maybe the novelization clears this up, by showing his thoughts maybe?
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Foster Novelization confirms it - he only did it because Leia asked.
Basically, the ONLY reason he didn't tell her "No, what glitterstream have you been sniffing?" is that he was afraid she would dump him again, permanently.
He wanted to laugh derisively. If he did, he knew she might never speak to him again. “Me? No. If Luke couldn’t reach him, with all his skills and training, how can I?”
She was nodding slowly. “Luke is a Jedi. But you’re his father. There’s still light in him. I know it.”
This is confirmed when we hear his thoughts when he's debating whether to confront Ren or not when he actually bumps into him:
A chance, then, to make it back to the Falcon before everything on this planet went to hell. A chance later for another reunion, on another world. A face swam before his, its features aged but still soft, the voice that emerged from between so-familiar lips biting yet always affectionate. Forming words that lingered in his thoughts. Forming, at last hearing, a request.
A request that wouldn’t go away, he knew. It would never go away. He made up his mind. Instead of retreating, he advanced. Instead of running for safety, he took up the challenge. There was no real choice, he told himself as he advanced to the edge of the walkway. And called out.