One obvious possibility is touch football. I know almost nothing about the strategy and tactics of football, but touch football seems to at least superficially match the general flow of full-contact football. That said, I'm not sure how the offensive and defensive lines would work in 11-man competitive touch football.
Isn't this a bit ... lame (no pun intended). I'm not a football fan, but violence is definitely part of what makes it exciting to me, when I do watch.
As a society, we need ways for people to get out aggression in a generally non-harmful way. Note that I'm not arguing against making football safer for players, but rather against the elimination of violent sport.
Maybe robo-football? There's just something fun about beating a consenting opponent to the ground.
I've started playing flag football after playing football 10 years ago. I've stopped playing football because I tore my ACL in both of my knees.
Beeing a defensive end / outside linebacker I can say that the bigger positions don't really translate to flag football. You can't really block other people without real contact. We are playing 5 on 5 - but I can't imagine how contact less football would work 11 on 11.
I enjoy playing some flag football, because it's a nice workout and some of the aspects of football are in (different coverages, beating routes...)