First of all, it is likely that a ban on plastic bags would not necessarily lead to greater use of paper bags. Many people use bags made from canvas or from other kinds of cloth. Such bags are sold at grocery stores and elsewhere.
Even if paper bags were to replace plastic, you could argue that they are not as bad for two reasons. First, they are biodegradable. Plastic bags will stay around forever, doing things like floating around in the ocean and causing damage to birds and turtles and such. Paper bags will not. Second, they are made from a much more renewable resource. Trees can be farmed, so making a paper bag does not necessarily mean cutting down a tree in some beautiful forest. Plastic, of course, is made from petroleum.