Geoffrey's mother is Conan's first wife (name not known).

From Cokayne's "Complete Peerage", in the article on Richmond:
"In the 11th century and the early part of the 12th the rulers of
Brittany styled themselves indifferently "Duke" or "Count"; thereafter
"Duke" became the rule. The English chancery, however, as also the Papal
and French, continued to use the older style of "Count". In the present
article the term "Duke" has been used throughout in order to avoid
confusion with the comital style applied to other members of the
family."
I do likewise in this genealogy.

Per Galliou and Jones' "The Bretons", when Geoffrey departed for Rome on
a pilgrimige from which he never returned, he left his sons, ALAIN and
EUDES under the protection of RICHARD II, DUKE OF NORMANDY (RIN
1306), who also proffered assistance during the last Viking attack on
the duchy in 1013-14. Later, under ROBERT I (RIN 1323) (1027-35),
relations between Brittany and Normandy deteriorated, but were
eventually patched up.

References: [AR7],[PlantagenetA],[ES],[Weis1],[Theroff],[RFC], [YorkshireV]