A public franchise is a sort of state-sponsored monopoly. Public franchises can be in areas such as drinking water supply, or perhaps most prominently, in the U.S. Postal Service.
A public franchise is created when a government restricts a market to a single firm, which it appoints. Any other firms are prohibited by law from competing.
Public franchises are put in place to strictly regulate a certain market. This could possibly help consumers by keeping prices low and possibly subsidizing costs, or it could not. Ideally, the government is ensuring the public gets the best provider for the best price.
The effect of a public franchise on the market is variable. Because a public franchise is a kind of monopoly, it automatically makes the market less efficient. Because such a firm has no competition, its prices no longer reflect supply and demand.