It's a stretch to call drunken fans chanting insults at their rivals to the mangled and barely recognizable tunes of 40 year old pop songs "football songs". I'd also call it a stretch to say a song becomes a football song because EA Sports decided to put it in a video game soundtrack.
Football songs I like
(1) Three Lions by the Lightning Seeds - it's really an ingenious pop song that captures the mindset of any football fan quite brilliantly
(2) World in Motion by New Order - a classy pop song with a catchy hook and an even more memorable rap by John Barnes
(3) Un'estate Italiana by Gianna Nannini & Edoardo Bennato - Late 80s Italian power pop with plenty of schmalzy pathos which however does strike the exactly right notes to create a sense of nostalgic longing for that particular Italian summer 1990 (this song was unsurprisingly quite popular in Germany that summer).
(4) 54,74,90, 2006 by Sportfreunde Stiller - Written in time for the 2006 World Cup, this is the he first and only decent song about Germany's national team. It was written by a pop band whose members happen to be big football fans and unlike most football-related songs this was not commissioned by an organizing committee or FA. It represents the brief moment in time when the German national team managed to be a factor in 'cool' contemporary German youth culture. And it's pretty catchy.
(5) Zeit dass sich was dreht by Herbert Grönemeyer - This was the 'official anthem' of World Cup 2006 and thus a work of commission. As a neutral song nevertheless written in German, it had a somewhat difficult time appealing to either the German audience (which at that time embraced Germany-centric fan songs) and the international audience (which couldn't understand the lyrics or had any familiarity with Herbert Grönemeyer as an artist). I did however think it's actually a pretty good song, and better than most 'official' songs for tournaments. I will grant that my sentiments about this song (much like with Un'estate Italiana) might be linked to having been completely caught up in the World Cup at the time and subsequent nostalgia about it.