"Formigny and Castillion did kill any hope for the English to come back on French soil."
No, what killed English hopes of reconquest was the same thing as what killed English hopes of hanging on to Normandy and Bordeaux in the first place- factional conflict within the nobility which soon exploded into the Wars of the Roses and occupied English affairs for the better part of the next forty years. Neither Formigny nor Castillion crippled England militarily; in both cases it lost only a few thousand soldiers, and within a few years English nobles were raising armies numbering in the tens of thousands. But they weren't raising them to fight in France, they were raising them to fight each other. Had they wished they probably could have reopened the war in France, in fact that possibility was a consistent theme of Yorkist propaganda.
"So what do you need for a battle to be decisive if it doesn’t settle a problem?"
A battle which settles nothing in the long term is not decisive. When Formigny and Castillion were fought the outcome of the war was effectively predetermined, which is why the battles weren't decisive.
Bookmarks