This is complicated. You must realise that English military power in France was, in no way, possible without significant alliances and arrangements with continental allies; these ranged from local interests such as burghers, to the Duc d'Bourgogne (Duke of Burgundy).

Successful English incursions into France tended to combine a mixture of English field armies with direct support from local interests. Henry V and Edward III both had significant luck in their 'invasions' of France.

Firstly, I will answer how England acquired Northern France, in the 1417-1420 campaigning period. Essentially, Henry V utilised the fractious nature of Valois-Armagnac politics to drive a wedge into Northern France. He acquired Rouen in a fierce siege, which cut Paris off from the mouth of the Seine. When the Dauphine's partisans assassinated John the Fearless, John's son (Phillip The Good) essentially turned to Henry and said 'well, looks like you're the best game in town' and offered his support. The royal court thereby agreed to terms; the French military leaders were too divided, in some ways still reeling from Agincourt, but mostly in a state of internecine disruption from the intrigues of the Valois and Armagnac parties. With the Treaty of Troyes, Henry V became Regent and Heir of the Kingdom of France. His next move was to actually enforce that; because, as you might imagine, the French didn't simply collapse and await conquest.

In 1421, an allied force of Scottish and French forces caught and destroyed a significant army under Henry's brother, Thomas, at Bauge. This forced another round of campaigning from Henry, who died while in the field in 1422. See, 'capital' is a modern term. All Paris was back then was the center of courtly administration and a military bastion. The vast majority of economic strength and military force was decentralised amongst the semi-autonomous duchies. Whilst this meant that France could be fractious and easily divided, it meant that a unification of opposition with significant resources was ALWAYS possible so long as large areas of the kingdom were unconquered.

Conquering France was not simply a case of 'knight takes king, I win'. It was a complex, diverse, gigantic area with thousands of competing interests. If the English could appeal to the majority, they remained in power. If the Dauphine's forces, with their control over the majority of modern France, could pull together, they would oust the English with ease.

Do you see? The English had to not only maintain a hundred alliances, they had to convince these local interests to consistently fight their countrymen. In contrast, the Dauphine's forces were far closer to the war front, and thereby much easier to bring to bear.

The English response worked well until the build up of French resolve and the dissolution of their alliance with Burgundy. When the French encroached upon English territory, or if the Dauphine's territories were judged to be vulnerable and Burgundian aid was assured, an expedition would be sent from England, which would then join with the English 'field army' in France, further aided by Norman garrisons. This force would defeat or push back the French forces, and follow up to conquer French possessions. Verneuil was a case of the French attempting to relieve a fortress, being intercepted and defeated, while Orleans was a case of an English-Burgundian force being out-manoeuvered by a counter-attacking French army.

When the English could no longer court local interests or finance the expensive expeditions, their power toppled, piece by piece. On the 13th of April, 1436, the citizens of Paris threw open their gates to admit the forces of the Dauphine, ending the English occupation of Paris.

Edit: Much to my chagrin, Phillip the Good was not, indeed, a 'Godd'.