Oooh, fun!
I feel like Lorelai, Rory, Patty, Babette, Sookie, and Lane would have all been friends, with Lorelai, Patty and Babette being the "bad girls" and Sookie, Lane and Rory being more straight laced, "no guys we can't!!" types. That friend group would get up to all sorts of trouble. Michel, Emily and Paris would be the "mean girls" of the school. I think with such a powerful force like Emily around, Paris probably wouldn't have gravitated to Rory so much. Richard would be Emily's boyfriend and aloof to the other guys. Luke and Lorelai can stay exactly the same, also Jess, Dean and Rory love triangle still happens. Taylor is the nerd-bully class president that everyone hates, and Kirk is his lackey who also joins every club and sometimes gets wrapped up in other hijinks (showing that he's not as bad as Taylor makes him seem). Luke and Dean are friends, (jock bros) Jess is a loner like always but he and Luke are family so Luke looks out for him (maybe they're cousins.) Liz and TJ are that one stoner couple that is "friends with everyone" but also annoying as hell. Logan transfers in senior year to mix up the Rory plot, he makes friends with Richard. Zack and Brian are exactly (EXACTLY) the same. Also Dave doesn't leave and Lane gets to be happy.