what happened to the wife and kid??

He says he "lost" them. That could mean several things. Perhaps she discovered his bigamy. It's possible they died - although how the child would have is a mystery. But I think the likeliest reason is that there came a point in his penury where he couldn't face them anymore and he scarpered. Verdoux was not a pleasant person. And, although he clearly cared for his family, I think it likely that a man of his calibre would allow vanity to overcome conscience in a situation like that.

Critic Andre Bazin theorized that Verdoux killed them as well.