Well, it'd depend on who Henry of Monmouth (OTL Henry V) marries, with less success or drive in France a match with Catherine of Valois and the attendant Treaty of Troyes is unlikely, and with that we don't get the schizophrenia and such (what other brides are there?). In any case I'm unfamiliar with his military abilities as compared to his son, and what he can do in France is hampered by rebellions at home, which are stoked to some extent by his status as a usurper and the fake Richards floating around.
Or, if Monmouth (or his younger brother Humphrey- a successful commander OTL) lives long enough they could very well meet with some success in France, but whether, without the aura of kingship, he can garner the military support necessary to consolidate his gains is questionable.
In any case regency is always negative (and going by the life of OTLs Henry VI necessary) and met with acrimonious infighting which, even if it fails to reach outright civil war it doubtless damages the country, and the French, once they get a sane king, will seek to take things back. That said a c. 10 yr-old is easily better than a baby. In this other family members will be key, if the boy's uncles John of Lancaster and Humphrey of Gloucester feud, plus the Beauforts and, and ...
So, the characters behind the Wars of the Roses are still floating around, but their actions might be altered. In any case a mentally-healthy king in a shorter regency is likely better for everyone, but I was always sceptical of England's ability to hold onto France.