Complex sentence: His cousin, Arnulf, archbishop of Rheims, was illegitimate, while the counts of Vermandois were direct male-line descendants of Charlemagne through Bernard, king of Italy, the illegitimate son of Pepin of Italy.
Split into simpler sentences: His cousin, Arnulf, archbishop of Rheims, was illegitimate. The counts of Vermandois were direct male-line descendants of Charlemagne through Bernard, king of Italy, the illegitimate son of Pepin of Italy.