Indeed, you'd probably expect it to be the other way round, but the color orange was named after the prominent tone of the orange fruit when it's ripe.
The word 'orange' evolved from orenge, an old French term for the fruit. The earliest use of orange as a color was in a 1512 will, which marks the point when its usage for the color began to grow in the mainstream.
Before the popularization of the word orange for the colour, it was distinguished between two shades; yellow-red for the darker orange, and yellow-saffron for the lighter, yellowish orange.
Bonus fact: Did you know that there's no single English word that truly rhymes with orange?