Connor and Duncan MacLeod seem to be somewhat related (they are of the same Highlander clan).
Were there any other Immortals in the Highlander franchise who were related to at least the same degree, or were the MacLeods an exception?
They were not related, but they were raised in the same clan. According to Wikipedia:
In the eleventh episode, "Family Tree", Duncan's father and Chieftain of Clan MacLeod, Ian MacLeod, states that the newborn Duncan was a foundling given to his wife Mary to replace the stillborn son she had delivered, and raised to be his successor.
Essentially, he was adopted.
I don't recall of anything else similar from the films or TV show, however.