Your planet is closer to its sun
Okay, so just being a bit closer to the sun alone will not give you a violet sky, but it does two really important things. It will increase the amount of water vapor in the air and it will make the polar regions the primary habitable zone of the world since the tropics will be too hot for any Earthling visitors. Purple skies here on Earth are caused by the way light scatters when our yellow sunlight hits a sky full of a combination of gaseous and crystalline water in the air at an acute angle.
Here on Earth, our poles get a perpetual twilight that typically looks like this:
Because of how cold the air is you don't get a lot of water vapor to scatter the light, but if the North pole had a temperate environment, it would look more like this for the 6 months of the year that you get sunlight:
Technically speaking, this world would still have generally blue/white or maybe even entirely white sky at lower latitudes, but in the regions that people could safely call home, it would be all purple all the time.