Although WFRP 1 The Enemy Within calls Karl Franz the great greta grandson of Wilhelm III (or to be precise, the great great present grandson - due to a print error), I would rather favour seeing Wilhelm III as his great grandfather, and merge Matthias IV and Mattheus II.
The line of successors to Wilhelm is a bit unclear, and, as so often, various sources contradict each other. No surprise really, given the changes between WFRP 1 & 2, and the fact that there does not seem to have been strict coordination between WFB, WFRP and the Black Library novels.
Matthias the IV, named in Beasts of Velvet as the immediate successor of Wilhelm III, disappeared (according to WD 140) in 2401, 28 years before Wilhelm came to the throne. The father of KF is usually named Luitpold, but Letters from Sylvania calls him Ferrand.