Keeping the hold on France would be REALLY hard. Not only it depended a lot from Burgundy alliance (and regarding the more or less changing policies and interests of the duke, it was unreliable at best) but Charles VII had sumply too much territories, too much allies and too much possibilities to take back the North.
Don't forget that English army had to plunder the country in order to have enough ressources to fight the constant french attacks from south, and that's not really going to make the population accepting an english king.
OTL, the Normandy was by exemple one of the region with an actual organised resistance against the Lancasters.
But, even in Paris that wasn't really favourable to the Armagnac faction, it was more about a support of Burgundian faction than a support of Henry who was particularly hated or at best having a bad reputation and picture.
For me, a continous campain in France would even formed more quickly a civil war or at least a noble unrest in England as it would have increased more quickly and more importantly the raise of funds in England.