In January 1027 she married Richard III, Duke of Normandy. The marriage was short-lived for on 6 August of that same year Richard III suddenly died. Adela secondly married Baldwin V, Count of Flanders in 1028.
Adèle’s influence lay mainly in her family connections. On the death of her brother, Henry I of France, the guardianship of his seven-year-old son Philip I fell jointly on his widow, Ann of Kiev, and on his brother-in-law, Adela's husband, so that from 1060 to 1067, they were Regents of France.
- Baldwin V, Count of Flanders (1012 – 1067). Married Adèle of France (1009-1079), and had issue, Baldwin VI, Queen Matilda and Robert I of Flanders.
- Mathilde (born between 935 and 945, died 25 May 1008 in Ghent, buried in St. Peter's church), married:
His father, Arnulf I had made Baldwin co-ruler in 958, but Baldwin died before his father and was succeeded by his infant son Arnulf II, with Arnulf I acting as regent until his own death. Then Baldwin Balso continued as the regent for the child.
During his short rule, Baldwin was responsible for establishing the wool manufacturing industry at Ghent and markets at other towns in Flanders. Baldwin III died on 1 January 962. After Baldwin's death, Arnulf I arranged for King Lothair of France to become the guardian of Baldwin's son Arnulf II.
Through his mother he was a descendant of the Anglo-Saxon kings of England, and through his father, a descendant of Charlemagne. Presumably Arnulf was named after Saint Arnulf of Metz, a progenitor of the Carolingian dynasty.
At the death of their father in 918, Arnulf became Count of Flanders while his brother Adeloft or Adelolf succeeded to the County of Boulogne. However, in 933 Adeloft died, and Arnulf took the countship of Boulogne for himself, but later conveyed it to his nephew, Arnulf II.
Arnulf I greatly expanded Flemish rule to the south, taking all or part of Artois, Ponthieu, Amiens, and Ostrevent. He exploited the conflicts between Charles the Simple and Robert I of France, and later those between Louis IV and his barons.
In his southern expansion Arnulf inevitably had conflict with the Normans, who were trying to secure their northern frontier. This led to the 942 murder of the Duke of Normandy, William Longsword, at the hands of Arnulf's men. The Viking threat was receding during the later years of Arnulf's life, and he turned his attentions to the reform of the Flemish government.
- Hildegarde, born c. 934, died 990; she married Dirk II, Count of Holland.
- Liutgard, born in 935, died in 962; married Wichmann IV, Count of Hamaland.
- Egbert, died 953.
- Baldwin III of Flanders. (c. 940 – 962). Married Mathilde Billung of Saxony (c. 940 - 1008), daughter of Hermann Billung, and had issue,
Arnulf I, skipping one generation.
- Elftrude; married Siegfried, Count of Guînes.
The early years of Baldwin's rule were marked by a series of devastating Viking raids into Flanders where little north of the Somme was left untouched. By 883 he was forced northward to the flat marshes of the pagus flandransis which became the territory most closely associated with the counts of Flanders from that time on. Baldwin constructed a series of wooden fortifications at Saint-Omer, Bruges, Ghent, and Courtrai and seized those lands abandoned by royal and ecclesiastical officials. Many of these same citadels later formed castellanies housing government, militia and local courts.
- Arnulf I of Flanders (c. 890–964), married Adela of Vermandois
- Adalulf (c. 890–933), Count of Boulogne