The thing is we know Charles VIII of France was definitely fertile, 4 children by Anne of Brittany over 7 years, with 3 over a period of around 3 years shows he could definitely father many children. And something else to consider about his fertility, Anne of Brittany only had 3 out of around 15 children survived past birth, so I am going to guess that there was something wrong on her end.
And so, with Elizabeth, even if Charles still dies in 1498, he most likely has at least 4/5 children, most likely 6/7. Of these, there is probably more than half are that are male, so let's day 4 boys and 2 girls. The names would be pretty clear, Charles and Francis for the eldest boys (2 out his 3 sons were named Francis OTL), Louis, John and Robert would be good options for the other 2. For the girls: Anne, Margaret, Joan, Louise and Charlotte are all good options.
So, by this logic, the family would look a little something like this:
Charles VIII of France (b.1470: d.1498) m. Elizabeth of York (b.1466: c.1515/1530) (a)
1a) Charles IX of France (b.1486)
2a) Francis, Duke of Anjou (b.1488)
3a) Robert, Duke of Berry (b.1489: d.1490)
4a) Anne of France (b.1491)
5a) John, Duke of Berry (b.1493)
6a) Margaret of France (b.1496)
As for the issue of England, Charles most likely does not support Henry Tudor and thus he ends up dying in obscurity, secure in the knowledge he was never going to be king. However, another option for him would be to support the accession of Elizabeth, who would be the one that was meant to be in line to the English Throne. In her stead, Cecily of York is most likely created Queen of England with Edward, Earl of Warwick as her co-monarch. If Henry Tudor proves himself, he may become the Earl of Richmond and might even be rewarded with the hand of Anne of York.