Call in a pro for an estimate. If the burn is into the wood, then sanding won't get it out. I cannot say without looking at.
You can either spot sand the area, try to match the stain and re-poly, or if the burn will not sand out, you may have to replace the boards in question, sand, match the stain and re-poly. Problem is you will now likely have a noticable repair job.
I have a noticable repair job from previous owner who replaced one parquet square because of dog urine. He used the same stain and process he used on the floor originally, but ist noticable. At least the rug in the dining room covers it so its not a big deal.
Depending on where the burn is located, the professional may recommend a specific type of repair.