Are there any natural ways to ease pain in the foot while running?

Proper footwear. Supportive shoes and orthotics if not due to injury like a sprain or fracture. Ice is helpful after run to reduce inflammation and swelling. Need to find out cause of your symptoms. See a podiatrist.
Shoes. Good fitting running shoes. I suggest you go to a specialty store for runners.
Yes. Often times using an orthotic or support in the shoe will help ease the pain.