Nicknamed for the sprig of broom (= genêt plant, in French) he wore in his hat as a badge, at the age of 15 he married Matilda, the daughter of Henry I of England and widow of Henry IV, Holy Roman Emperor. The marriage in 1128 was meant to seal a peace between England/Normandy and Anjou. She was eleven years older than Geoffrey, and their marriage was a stormy one, but she survived him. Their eldest son became Henry II of England.
The year after the marriage Geoffrey's father left for Jerusalem (where he was to become king), leaving Geoffrey behind as count as Anjou.
When king Henry died in 1135, Maud's cousin Stephen seized the throne. While Maud turned her attentions to England, Geoffrey focused on the conquest of Normandy. This was to take a decade of steady seigework and alliance-building, a process Geoffrey would not abandon even when his wife pleaded for help in England. The merits of this strategy are sometimes debated. While Angevin forces might have been decisive if brought over to England, it also seems that the possession of Normandy played a role, possibly even a decisive one, in the eventual success of their son Henry in taking the English crown.
Geoffrey also put down three baronial rebellions in Anjou, in 1129, 1135, and 1145-1151. The threat of rebellion slowed his progress in Normandy, and is one reason he could not intervene in England.
In the remaining years of his life, Geoffrey consolidated his hold on Normandy, reforming the administration of the duchy, and, in 1150, introduced Henry into its rule.