The answer to this question depends on what you mean by 'resemble.' I would say that the soldiers would resemble each other, and the same types of soldiers (with one exception) were involved in the start and the beginning of the conflict, but the details changed dramatically.

In the beginning and the end of the war the English army was composed of archers and gentlemen-at-arms (knights and untitled gentlemen who fought like knights). The French armies at the beginning and the end of the war were composed of knights and an assortment of infantry, often foreign mercenaries. But by the end of the war, the French had added a large amount of field artillery, and used it to win battles (and the war).

Knights on both sides were equipped much the same way. In the early war (the battle of Crecy, say) they would have worn plate armour over mail. Their torsos would be protected by a coat of plates (small-ish plates riveted to canvas and covered by a richer cloth -- kinda like a Lorica Segmentata turned inside out). Their limbs would have been protected by simple plate defenses, and on their heads they would have worn a bascinet without a visor or a great helm. The English knights often fought on foot, beside their archers, armed with shortened lances and long axes. French knights fought on horseback, on (mostly) unarmored warhorses, carrying lances. Swords would be a side arm.

English archers in the early war would be almost entirely unarmored, and often lightly armed -- long knives, the hammers they used to drive in the stakes in front of them, etc.

I can't speak in detail to the Genoese crossbowmen that the French used.

In the later war, everyone had more and better armor. English and French knights/gentlemen at arms would be armed head to foot in plate armour, with visored helmets (great Bascinets and some armets, maybe some early sallets) and solid breastplates. Armour was more commonly heat treated, and with better methods, and was sometimes 'proof' against crossbow bolts (they would shoot the breastplate to show that it could protect against crossbows). Horses were sometimes armoured. For knights on foot, short lances and axes were replaced with specialized polearms, mostly the poleaxe (5-6 foot shaft with some combination of awl point, hammer head, axe head and pick-head).

Archers by the end of the war would often have a helmet, a jack (a linen armour with padding or multiple layers of fabric), a sword and maybe a bill or other polearm for close in fighting (English archers often fought defensively from field fortifications, so they would probably have extra weapons just lying close at hand).

I will get to cross-pollination of tactics on my lunch break, since I need to get to work.

Sources: The Knight and the Blast Furnace by Dr. Allan Williams Arms and Armour of the Medieval Knight by Edge and Paddock