Froideur is a state of being cool or aloof to other people. Your classmate may be smart and attractive, but their froideur makes it very hard to get to know them well.
Some people are warm and welcoming, while others have an aura of froideur, a chilly, distant, or haughty attitude that is quite the opposite. Examples of froideur include showing no emotion after a classmate's touching speech or greeting someone at your door with a cold gaze and an expressionless, "Yes?" In French, froideur means "coldness."