The word "braid" simply refers to a hairstyle where strands of hair are interwoven. A French braid is a specific type of braid where the strands are woven in a pattern that creates a three-dimensional, raised braid.
It's similar to how we call "jeans" jeans even though they come in many different styles and colours. "Braids" is a general term, and French braids are just a particular type of braid.