Here's my idea:
On the 3rd of April, 1461, the King of France finally was given a healthy Dauphin. Named John, this son would survive as the others had not and was followed by 4 more siblings, two of which (Charles, Duke of Berry and Joan of France) would also survive their infancy. And thus, the future John III of France was to begin. John la Grande, as he was known as a child, was quite intelligent and at the age of 9 presented his mother with a translation of the Gospel of John, showing his connection to John the Evangelist that stayed with him from his youth.
On the 18th of March, 1480, John la Grande watched his only sister Joan of France marry the Count of La Marche, future Duke de Bourbon. This marriage would remain childless and, when in 1495 the Duke de Bourbon applied to have his marriage annulled so that he might marry the Princess Anne of France, who was the child of John as the King of France.
As to the King's own marriage, in 1477 he rebelled against his father and married Yolande of Lorraine, after his father had gone out of his way to arrange a marriage between the Dauphin and Joanna la Beltraneja of Castille, who had fled to France in 1474 with the promise of a match between the two under her mother's guidance. Now without support, she returned to Castille in shame and on the last days of the year married her maternal uncle, King Afonso V of Portugal, giving him a single son in 1480, named Afonso.
With Yolande of Lorraine, John would have 8 children, of which 4 would survive: Anne of France (b.1482), Louis, Dauphin of France (b.1484), Francis, Duke of Anjou (b.1487) and Michelle of France (b.1492). Of these children, Anne would marry the Duke of Orleans in 1500, giving him 3 daughters and a son in the wake of his childless nature: Marie d'Orleans (b.1503), Claude d'Orleans (b.1509), Jacques d'Orleans (b.1510) and Renee d'Orleans (b.1513).
On the 1st of May, 1492, John III of France pushed and succeeded in finalizing the marriage between his younger brother and Margaret of Austria, after his first choice of Anne I, Duchess of Brittany ended with her married to the Holy Roman Emperor in 1490, and the couple had two sons: Arthur (b.1495) and Frederick (b.1499). With his bride Charles, Duke of Berry would have only one child, Marie de Berry (b.1498) before he died of a fever that same year. His bride would remarry to the Duke of Savoy, before retreating into a convent.
In 1485 John III supported Henry Tudor to the Kingdom of England, with the strict promise that Henry's eldest son would marry a daughter of the King of France. This wish came true in 1502, when Arthur Tudor married Michelle of France, the 10 year old Princess. Arthur would die young, aged 20, in 1506 and his widow, still physically a child and not having consummated the marriage, went on to marry his younger brother Edward, born 1488, the year after.
His son and heir would marry, in 1500, the Infanta Catalina (Catherine) of Aragon. The couple would undergo 9 recorded pregnancies, of which only 2 children survived: Charles VIII of France (b.1506) and Louise of France (b.1512). To add to this situation, the King's only brother Francis, Duke of Anjou suffered a great fall in 1511 and died, aged 24. This ended his betrothal to the Princess Mary Tudor.
Louis XI of France (b.1423: d.1483) m. Margaret Stewart of Scotland (b.1424: d.1445) (a), Charlotte of Savoy (b.1441: d.1483) (b)
1b) Louis, Dauphin of France (b.1458: d.1460)
2b) Joachim of France (b.1459: d.1459)
3b) Louise of France (b.1460: d.1460)
4b) John III of France (b.1461: d.1522) m. Yolande of Lorraine (b.1460: d.1510) (a)
1a) Joan of France (b.1479: d.1481)
2a) Anne of France (b.1482) m. Louis, Duke of Orleans (b.1462: d.1515)
1a) Louis d'Orleans, Count of Blois (b.1502: d.1505)
2a) Marie d'Orleans (b.1503)
3a) Miscarriage (c.1505)
4a) John d'Orleans, Count of Blois (b.1507: d.1508)
5a) Claude d'Orleans (b.1509)
6a) Jacques, Duke of Orleans (b.1510)
7a) Renee d'Orleans (b.1513)
3a) Louis XII of France (b.1484: d.1540) m. Catherine of Aragon (b.1485: d.1536) (a)
1a) Louis, Dauphin of France (b.1504: d.1509)
2a) Charles VIII of France (b.1506)
3a) Miscarriage (c.1507)
4a) Louis of France (b.1508: d.1508)
5a) Francis of France (b.1510: d.1510)
6a) Louise of France (b.1512)
7a) Miscarriage (c.1513)
8a) John, Duke of Anjou (b.1515: d.1520)
9a) Miscarriage (c.1518)
4a) Francis, Duke of Anjou (b.1487: d.1511)
5a) John of France (b.1490: d.1490)
6a) Michelle of France (b.1492: d.1518) m. Arthur Tudor, Prince of Wales (b.1486: d.1506) (a), Edward VI of England (b.1488: d.1543) (b)
1b) Margaret Tudor (b.1510)
2b) Isabelle Tudor (b.1512)
3b) Henry Tudor, Prince of Wales (b.1514)
4b) Mary Tudor (b.1515)
5a) John Tudor, Duke of York (b.1517)
7a) Miscarriage (c.1493)
8b) Marguerite of France (b.1496: d.1497)
5b) Joan of France (b.1464: d.1505) m. Peter II, Duke of Bourbon (b.1438: d.1503) (a)
6b) Louis of France (b.1466: d.1466)
7b) Charles, Duke of Berry (b.1470: d.1498) m. Margaret of Austria (b.1480: d.1530) (a)
1a) Louis, Duke of Berry (b.1497: d.1503)
2a) Marie de Berry (b.1498) m. Charles III, Duke of Bourbon (b.1490) (a)
1a) Marguerite de Bourbon (b.1517)
2a) Francis I, Duke de Bourbon (b.1519)
3a) John de Bourbon (b.1520)
4a) Anne de Bourbon (b.1522)
5a) Miscarriage (c.1523)
6a) Sophie de Bourbon (b.1525)
8b) Francis of France (b.1472: d.1473)