Insouciant

Etymology

From French insouciant: in- ("not") + souciant ("worrying"), from soucier, "to trouble" (ultimately Latin sollicitare). Literally "not worrying." English kept the French spelling and the faint air of Continental cool.

adjective · /in-SOO-see-unt/
Casually unconcerned; breezily free of anxiety.
What it names
A studied lightness in the face of things that ought to worry you — sometimes charming, sometimes maddening.
Example
He gave an insouciant shrug at the deadline, as if it were happening to someone else.
Related idea
Nonchalant is the everyday synonym; insouciant is a touch more elegant, even affected.