Is mouthwash supposed to foam up when you gargle?

Probably some brands probably yes, such as those containing hydrogen peroxide. Others no. This is personal preference, not a health issue.

The action of the Hydrogen peroxide used as a cleaning and disinfecting agent causes the foaming. The foaming effect aids in loosening the food and bacteria in and around the teeth.

That depends on the mouthwash. If mouthwash contains foaming agent or hydrogen peroxide, the answer is yes. Please note that mouthwash is an adjunct to, not a replacement for, proper brushing and especially flossing.