I know Francisco leaded him to meet largo cause he doesnt really want to be king, but from Zenjiro perspective, its still in his benefit if Francisco becomes king, not only cause they have cordial relationships, but cause Zenkichi already has double bloodlines and Francisco would normalize the threat of double bloodlines among other countries way before he has to rise to the throne.
Cause Eventually Carlos will become crown prince and he having two bloodlines will become an issue, not even talking about all other Zenjiro children.