Food poisoning typically will not affect breastfeeding a child. The typical symptoms of food poisoning - vomiting and diarrhea - are symptoms specific to the digestive system. Both come from the need to expel the bad from the body. In general, the symptoms stay within the digestive system or are the body simply trying to get rid of the bacteria; that’s what a fever is - trying to overheat the bacteria.
The only time food poisoning might affect breastfeeding a child is when it gets into the bloodstream. By this point, however, the mother would be in the hospital. Typically, you never want to stop breastfeeding until you’re ready to wean the child off of breastfeeding, but in serious cases of food poisoning, it might be advisable to stop until it can be confirmed that she is no longer infected.