A Gallic shrug is actually a very particular kind of shrug, a fairly rude and aggressive shrug in this context. It’s a French way of saying, basically, “Not my problem.”

v. collectively or individually finding someone/something to blame for a problem, as opposed to brainstorming which connotes finding solutions to a problem

n. the act of finding someone/something to blame for a problem

(from a TV ad for HD television)