In OTL, the Congress of Vienna reverted France to largely its 1789 borders (plus the Comtat Venaissin). This meant that the Rhineland had to go to someone, and as rolling back the HRE's panoply of states was impractical (German mediatization was apparently one thing the reactionary powers agreed with Napoleon on), they basically just gave it to Prussia, which at the price of getting a substantial amount of Catholics suddenly had a really nice industrial base which would help tilt the scales of German ascendancy in their favor.
So aside from Prussia, what plausible scenarios can lead to the Rhineland going to someone else?