You have to understand that inertia was a concept that was not well understood in Newton's time. People implicitly assumed that a body in motion would slow down and eventually stop after some time without the need of external force. (They assumed this because friction was not identified as a kind of push/pull force that surfaces in relative motion exert on each other but as an intrinsic property of every body.) When Newton deduced the first law it was a break from the past - a completely new way of thinking - and that is why (probably) he gave it a law of its own.
You are correct, the first law is not valid in a non-inertial frame. Think of yourself accelerating in a vehicle and looking at a rock on the street. The rock is accelerating in the opposite direction (in your eyes) and yet there is not external force acting on it.