Treks to see local culture?

We want to see Fansipan and local culture but avoid any artificial shows. What do you suggest?

I'd recommend combining Fansipan cable car with a trek to a more remote village such as the Sapa to Ta Van Village trek. But to be honest Sapa has become quite touristy in recent years, and given your limited time, it may not feel as untouched as you might expect. For a less touristy area I'd recommend Ba Be National Park instead.