At the time of his birth in 1365 little Edward of Angouleme was the prospective King Edward V of England. Son of Edward the Black Prince, grandson of King Edward III, the little boy would have been expected to follow in his forefather's military footsteps – batter the French and help reclaim the lands of the Plantagenets.
Born when his parents were residing in the Duchy of Aquitaine, Edward was the first legitimate son of the Black Prince. His mother on the other hand, Joan of Kent, had already been married before and had four children from her first marriage. Her match with Prince Edward had caused a bit of a scandal, but that hadn't stopped King Edward from celebrating the birth of this new grandson and future heir to the throne. In Aquitaine the celebrations including a tournament of forty knights competing in honour of Joan, and a further 700 knights showing up to join in the celebrations.
Edward was christened by the Bishop of Limoges with a host of lords in attendance, as well as the King of Cyprus. It's difficult to tell where his household was set up, but Joan appears to have spent a lot of her time in Angouleme when she wasn't travelling with her husband. It's quite possible that Edward's home was set up in his place of birth, and Joan stayed near him when she could. Two years later Edward became a big brother when another son, Richard, was born.
The little prince's life was cut short around the end of 1370 (some chronicles state September 1370, others say January 1371). It was a short and sudden illness, possibly bubonic plague. Joan's whereabouts aren't known but she was probably near her son's household while he was ill. If it wasn't plague then she may even have nursed him through his final illness.
Sadly Edward's sudden passing coincided with his father, already a sick man, suffering a severe decline in his health. The Black Prince was encouraged to return to England for the sake of his health, and he and Joan quickly packed up and took a ship back to England with little Richard in tow. It was left to John of Gaunt, another of King Edward's sons, to arrange the funeral and burial of his infant nephew in Bordeaux.
It wouldn't be his final resting place, sometime in 1389 Richard had his brother's remains exhumed and returned to England to be buried at King's Langley. They were then re-interred again in the 17th century after the church became a ruin. Given that Richard proved to be extremely unpopular, it's interesting to speculate whether Edward of Angouleme would have been any better.