Depends on what you're into.
Common general post-game things people do is stuff like try to get a high win-streak in the regional battle facility (the Maison in this case), complete the PokeDex, shiny hunt, battle other players online, or just breed a bunch of stuff for varying reasons. Could always like, do E4 re-runs or buy all the clothes or something too, idk.
There's also the Looker Missions to do, which is something I recommend that everyone with a copy of XY do at least once in their life.