re: Antique Country French Hutch

If you can pull the top out without damaging it, you could try cutting some dados and grooves in the bottom to see if you can flatten it using cauls.   Adding some moisture to the concave side while you try to flatten may help as well.   If you can get it flat enough, you could then glue some wood strips into the grooves to stabilize it and maybe add some metal battens (angle iron or U channels)  for extra support.     

 If you are going to replace it anyway, you may not have much to lose from trying.   ( And I really want to know if this technique works 😀)