Union football perhaps, association football is what we call soccer.
The game without codification of rules dates back centuries (likely to the middle ages, first written accounts ~800 years ago). Codification by the Football Association (which is why it is referred to as Association Football) occurred in the mid 1800's. Shortly afterward, a football union was called (as they could not refer to it as an association) to codify rules of Rugby Football, which had been around for about a century, where players were allowed to carry the ball.
If you can find a means of demonstrating that early-mid 1700's occurred before the early 1200's you can claim that rugby came first.