Oldest College Football Programs . championship that season (against a Delaware team with some guy named Joe Flacco at quarterback). the teams that play in the final College Football Playoff The New Year's Six includes six of the ten oldest. of Championship Subdivision play, see NCAA Division I FCS football season. A college football game from between the Kansas Jayhawks and the Missouri Tigers. College football is American football played by teams of student athletes fielded by American .. Game between Stanford and California is the oldest college football rivalry in.