Domenic seems to have sumed up everything.
Basically, Louis VII having a son with Eleanor means that son (probably called Louis or Philip) will be the next King of France but also the next Duke of Aquitaine, provided Louis and Eleanor do not have a second son (a splitting of the inheritance would still be possible in that case). This wouldn't forcibly cancel the annulation of Louis VII and Eleanor, but would mean Aquitaine will have a stronger link with France.
Henry II is gonna be a bit weaker ITTL. I'm not sure he would marry Eleanor after her divorce from Louis VII : the fact she left Louis a son would probably reduced her attractiveness as a possible bride since her Duchy wouldn't stay with her second husband's children after her death.
As Domenic pointed out, Henry II not having Aquitaine won't probably change things much regarding his coronation as King of England. He will still be Count of Anjou, Maine and Tourraine as well as Duke of Normandy furthemore, and will probably make it so Britanny falls under his wing like OTL (when he married his son Geoffrey to Duchess Constance).
I'm wondering if that wouldn't butterfly Capetian-Plantagenêt rivalry... Probably not as their will still be the issue of Anjou and Normandy being vassals of the French King. But it wouldn't reach the scale it had OTL though.
Jackson said:
Also, Eleanor d'Aquitane and Louis VII hated each other, so if they have a son, that is the only child they are likely to have together.
They didn't hated each other : they just had non-matching personnalities.
Eleanor was a Southern Woman while Louis VII was a Northern man. In the Middle Age, Southern France was culturally richer than the North, who was military stronger on the other hand. Northern and Southern Feudal Lords never really got along in France, and that hartred can be clearly shown during the Cathar Crusade which happened several years later, as it was seen by the Languedocian as a Northern Invasion.
Plus Eleanor was rather cultivated woman, was rather strong-willed and had a love of arts. She also liked to have an oppulent life, having been born in one of the richest families of France.
Louis VII, on the other hand, had first started a career in the Church as he wasn't supposed to be king : the accidental death of his elder brother Philip made him heir then King to the French throne. However, his religious teachings marked his personnalities. Eleanor even said she had been married not a man but a monk.
Lastly, Eleanor had troubles adapting life at the French court. She was from the South in a court where they were plenty of Northen Nobles, and as I pointed out, the two sides of the Loire didn't get along well. Not to mention a meridional women already had left a dark mark in French history : Constance of Arles, third wife of Robert II of France and one nasty bitch. Thus, there probably was some sort of defiance against her at the court.
The marriage of Louis and Eleanor only started to fail during the Second Crusade, when Eleanor showed she was very close to her uncle Raymond of Poitiers, prince of Antioch. So close that rumors said Eleanor had shared her uncle's bed. And even after that events, you still had to wait 1154 before Louis VII and Eleanor had their marriage annulled, after several tries of recounciliation.
One correction also : that son wouldn't be the only child of Louis and Eleanor. Eleanor had two daughters by Louis VII : Marie (1145-1198), who married Henri I of Champagne, and Alix (1150-1195), who married Theobald V of Blois.
Plus, Eleanor later had eight children with Henry II of England and they weren't exactly love-birds...