The compositions of the English armies varied considerably throughout the war, but they were largely composed of Englishmen and occasionally Welshmen. The high-level officers and administrative personnel in England's continental holdings were almost always English noblemen, though the lesser officers — such as stewards, judges, garrison commanders, and provosts — were typically recruited from among the local French nobility.
The local Gascon nobility were rather fair-weathered and became increasingly unreliable as the war stretched on, though there were about two dozen great noble families (namely the lords of Albret) that provided the bulk of the continental soldiers for the English. The prominent Gascon nobility often switched allegiance to whomever appeared to be the likely victor and by the later stages of the war, they were rarely depended on. There was a great deal of local rivalries and petty disputes that dictated allegiances more than the French or English governments' interests, and thus diminished the actual number of soldiers that the duchy could provide.
Regardless, the English kings made great use of their Gascon vassals early in the war. When the English continental holdings were threatened, the English would recruit Gascon companies (consisting of 10–60 men) at short notice to carry out military objectives such as defending castles or towns, besieging an enemy position, or conducting raids. These forces would only serve for a short period of time — less than two months — and were then disbanded. Most of these levies were drawn from the retinues of the local Gascon nobility and they soon developed into a class of professional soldiers. These companies would be combined into larger groups for up to a thousand men, and larger forces could be assembled if time allowed for a longer recruitment period.
The Earl of Stafford's campaign in 1352 provides a good illustration for the personnel capabilities of Gascony. Stafford was able to assemble 3,800 soldiers levied from the Gascon nobility, in addition to perhaps some four hundred men from England. Sumption notes that Gascony could have likely provided anywhere between 4,000–7,000, but this depended almost entirely on the loyalty and enthusiasm of the Gascon nobility and the number of soldiers raised by Stafford was likely typical of the duchy. In fast-moving campaigns like Stafford's, it was often easier to just pull men from the continent. In larger expeditions and battles, the soldiers would have largely been drawn of England. At Poitiers, the English force consisted of 2,000 English and Welsh archers, 1,000 Gascon infantry, and 3,000 men-at-arms, of which perhaps half or a little less than that were English. However, at other major engagements, the bulk of the soldiers were brought over from England.
The aforementioned "professional class" is an important factor when speaking of the Gascon companies. As the soldiers gained experience and skill, they began forming what was effectively mercenary companies to be hired by any king or lord willing to pay them. While the French often referred to these companies as English, they were largely comprised of Gascon soldiers, but also included soldiers from England and other regions of France. These companies found service with both the English and French, and also found battle in the concurrent wars in Iberia and Italy. In France, these companies either roamed from town to town, raiding and ransoming on behalf of whomever was paying, or also provided garrison duty. Many of these companies soon devolved into bandit companies called routiers, while others gained more prestige like John Hawkwood's White Company.
Sumption, Jonathan (1990). The Hundred Years War 1: Trial by Battle.
Sumption, Jonathan (1999). The Hundred Years War 2: Trial by Fire.
Rogers, Clifford (2014). War Cruel and Sharp: English Strategy under Edward III.