If Henry V had invaded France, he probably would have focused on establishing English control over the whole of Ireland. Henry may have attempted the pacification of Wales and used his prisoner James I of Scotland to maintain some level of peace on his northern border. At the beginning of his reign, England was in the middle of a 28 year truce with France that was not due to expire until 1424. Even if Henry had not invaded France, he would have been still been obliged to defend the remaining English territories in France. So peace would have depended on the attitude of the French. In OTL, there were war parties in both kingdoms who wanted to restart the war.
As for if the war with France was necessary, it would depend or whether or not Henry V could control the war party in England clamoring for war. In OTL, the war party was a factor in the overthrow of Richard II, who wanted peace with France. Henry IV was able to use the war party to secure his ascension to the throne. The war party looked upon the House of Lancaster as a dynasty that would actively war with France. Also a successful invasion of France was considered by many in England as the only way to achieve a beneficial peace.
In OTL, Henry V extended an offer of marriage to Isabella of Portugal (the future wife of Philip the Good, Duke of Burgundy) but the negotiations did not go anywhere. Perhaps in this TTL, Henry is more persistent in his negotiations and marries Isabella, which would butterfly away Charles the Bold.