Apple Carplay relies on the iOS (iPod Operating System), but since the Classic doesn't use iOS, it cannot make use of the Carplay feature.
But you should be able to connect the Classic via the USB port (note, USB - not aux. They're two entirely different things) and then, using the Mode button on the car's stereo to select the USB port and recognise the Classic as a USB device. That's the option I was using with my Classic until it failed (albeit not in a vehicle with Apple Carplay). Otherwise, how would anyone use an Android device in the car, because (unless I'm mistaken and very, very wrong) it too cannot use the Carplay feature?
I recommend that you check the handbook with the car, to look for the "connect a non-Apple audio device" option. There must be one. Either that, or the car's manufacturer has been somewhat short-sighted.
- iPod Classic to car's aux port - audio cable from the Classic's headphone jack to the aux socket of the car. Car stereo input mode is AUX
- iPod Classic to car's USB port - 30-pin cable from iPod dock connector to USB port on car. Car stereo input mode is USB