In a business franchise, who develops the product and business systems?

It depends on the type of business franchise.

In a business format franchise, the franchise will provide the franchisee all of the necessary things for a product + business system like marketing assistance, machines, supplies, etc ... An example of this would be a fast food restaurant or a retail store.

In a product distribution franchise, the work is all up to the franchisee. The franchise will provide the logo and the right to sell its product but leaves the rest of the work to the franchisee. An example of this would be a car dealership or a gas station.