Second wife was Estrith or Astrid (Margaret) daughter of Sweyn Forkbeard, Anglo-Danish King of England from 1013-1014, by his second wife, Sigrid the Haughty. He had no children by his second wife.

From "Debrett's Kings and Queens of Britain" by David Williamson, ISBN 0-86350-101-X, p. 43:
He was the first Duke of Normandy to be succeeded by undisputedly legitimate sons, first Duke Richard III, then Duke Robert II.

Scandinavian influence remained strong in Normandy, and in 1014, Duke Richard II welcomed in his Christian capital of Rouen a pagan host from Scandinavia which under the leadership of Olaf and Lacman had recently spread devastation over a considerable area of north-western Gaul.120