Henry VI and Normandy

Henry VI by the late 1440s begins to realize that the Lancastrian cause in France is practically lost. A treaty is proposed with Charles VII whereby England retains Gascony and Calais, but Normandy is returned to France upon payment of a large endemnity. Would the English have agree to this? Or would perhaps the more militant anti-French factions in England would have wanted to retain Normandy at all costs?
 
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