You can say either. "Julienne" is a specific process, though. "To Julienne a carrot" is to shred it in a particular way. It's like saying "cook an egg" versus "poach an egg." To poach an egg is to cook it in a particular way.
"Julienne" is specialized vocabulary, but it's pretty common. Many specialized fields have their own specialized vocabulary. I talk about a "pig," but a farmer knows the differences between a "pig," a "hog," a "sow," a "barrow," a "boar," a "gilt," a "weaner," a "feeder," etc.
It means to cut something into very thin pieces a couple of inches long. It's done precisely, the pieces are almost exactly alike. When my wife wants to julienne something, she doesn't use a knife. She uses a tool called a "mandoline," which uses a flat bar to push the vegetable against a fixed, wavy steel knife.
I checked Wikipedia, and it says the origin of the word "julienne" is unknown, while a dictionary says it is "probably" from the French name "Julienne."