Let me start with saying, yes, this is American style football. If you watch, play, or just have family that does, and live in the U.S.A., this is probably what you think of as football.

In my family, we don't discuss college football at all. It turns out my husband and I support teams that have a long standing rivalry between them. Since I won't make him things in his team colors (but have more than once offered to bead him a tie tack with his first initial "M" in colors like maize and blue)- when I do beading in team colors, it's usually either the Chicago Bears for him, or the Oakland Raiders for my dad.

Team colors are the easiest and most identifiable way to support a team without infringing on trademarked logos. You can go subtle, like the diagonal blocks bracelet for example. For my husband's Bears, I'd use DB11-201 White Pearl for the outline color and DB11-45 S/L orange and DB11-277 Luster Cobalt alternating for the inner squares.
You could also string a necklace, bracelet, headpin earrings or a keyring very quickly, even adding plastic football beads, or make something like this memory wire charm bracelet in your team colors with football themed charms.
If you aren't sure about the colors and your making it as a gift, ask the recipient what team they are rooting for, and then look it up online. You might not get exact color matches, but with the variety of beads available, you can get very close.

If you're thinking of a gift for a man, tie tacks for men who wear them, for more casual looks, beaded beads on a leather or braided cotton cord would work well.

These peyote or brick stitch patterns can be added as pendants, or made into pins or earrings. You can also use them in items with school colors for school fund raisers! Each pattern is a separate image. My favorite brown is s/l rootbeer- DB11-150!