I may be talking out of my ass here, but I'm assuming given the long periods of war between France and England there was probably a lot of military tech exchange/copy/evolution. I don't know enough about the weapon or period to know if it was parrallel evolution or who invented first or whatever, but not surprising that they're basically the same weapon.
Only to a point.
Due to the radically different terrain, England never invested as much into cavalry advancements as France did, hence why French Cavalry are always depicted as usually being more armoured then the English counterparts of the same era. When the feudal system was starting to break down for troops and the standard troop become a soldier of the state and not a soldier of a specific lord, England moved more towards the same route that Castile/Leon/Spain did and went for more lightly armoured but mobile cavalry, where as France continued to to invest in the "tank" mentality to stupid high levels where you literally had multi-layered rigid plate skirts going down to about shin level, and were admirably proofed to a point against firearms, though this made them rather expensive, and the rider was still a primary target as he could only be so armoured compared to the horse.
On an infantry level, they were more or less the same, though tactics radically differed.
