The beret was a traditional Human clothing accessory and a type of of hat, often associated with the French.
Ekosian Nazi Party Secretary Daras wore a black beret with a swastika pin. (TOS: "Patterns of Force")
One of The Doctor's daydreams in 2376 featured him was painting Seven of Nine, dressed in a smock and beret. (VOY: "Tinker Tenor Doctor Spy")
In 2399, Captain Picard wore a beret when he visited Stardust City undercover. (PIC: "Stardust City Rag")