Charles lent Henry 2000 men, money, etc. I find many books sating how but not why. I'm writing a paper on this and spent a while researching. The source you got the information from would be extremely helpful but is not completely necessary.
The Yorkist dynasty of England had established a very strong and stable monarchy after the years of instability of the Wars of the Roses. Rather like the UK rather welcoming the Revolution in 1789, as it would make France less of a threat, Charles VIII, by assisting Richmond in his attempt on the throne would, at the very least destabilise England and, possibly, renew the civil wars, thus making England less of a threat.