I do not think that would fare well for the Lancastrians, at all. But overall, it would have to be determined who would succeed him. I am pretty sure that Henry took most of the nobility over to England with him, including those few who were killed in OTL. If this is an overwhelming victory for the French, then there would probably be more noble losses for the English
Depending on how badly the campaign goes, the nearest possible candidate on the throne could be a child, for instance - Richard, soon to be the 3rd Duke of York, who was a child of 4 at the time of Agincourt. Though the English would probably no prefer a child king - but that is just one extreme.