Just to be pedantic here is a list of direct train connections FRA - CGN:

ICE 828 dep FRA 5:02am arr CGN 6:08am (not Sat,Sun)

ICE 914 dep FRA 6:32pm arr CGN 7:37pm (not Sat)

ICE 910 dep FRA 8:46pm arr CGN 9:46 pm (not Sat)

ICE 924 dep FRA 10:25pm arr CGN 11:28pm (not Sun)

And two ICEs departing from Wiesbaden with easy connections from FRA:

ICE 716 dep Wiseb. 9:49am arr CGN 10:47am (not Sun)

ICE 710 dep Wiesb. 6:49pm arr CGN 7:47pm (not Sat)

All other connections require a change at Cologne main station or Messe/Deutz.