With the World Cup on, this is a common phrase I want to be able to ask. Is it simply 你看足球了吗？Or 足球比赛？And do I need the 了 in this sentence? Including the 了 makes it feel like I'm asking them "do you watch football these days, as opposed to before when you didn't?" Or should I put the 了 after the 看 instead of at the end of the sentence?
"你看足球比赛吗？" = "do you watch football match?"
"你看了足球比赛吗？" = "have you watched the football match? " (看 is the verb, 了 is the verb particle indicates 'completion of an action-- 足球比赛 is the object that was being watched)
"你看足球比赛了吗？" put the object '足球比赛' between '看' and its verb particle '了'. that make '看足球比赛' a verb phrase
If you want to ask if someone watched the football match, #2 and #3 are both acceptable.
People recently are just referring to world cup matches as 球赛 which in English we might just call the game.
You already have the sentence structure down pretty well, so colloquially you could just say:
In day to day speaking the orders can be swapped for emphasis or clarity.
了 here isn't changing the state to the level that you feel like it is, because you're referring to a specific one ore two matches that have already happened - it's basically phrasing it into the past tenths.
If you remove the 了:
It sounds like an offer to watch a game together.