You do not need to install Apple CarPlay if it is supported in your vehicle. If your C3 is 2016 or later model year (2017 or later for C3-AirCross), then you just have to connect your iPhone to your vehicle's USB port and CarPlay will start. You should have minimum iPhone 5 with iOS 7.1 or later version.
If you have older model of C3, then you can't use CarPlay and there is no way to install it (that I know of). Only way then is to buy an aftermarket infotainment system with Apple CarPlay integration.