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The very short answer is they would have all dressed the same.This is a long time before any real sort of military uniform.However there are field signs and livery colours. The former in the context of the 100 Years War is the red cross for the English and white cross for the French..... BUT I don't think there was any real uniform way of displaying it. The popular perception is that the English wore the red cross on white, but I don't know how true that was - perhaps later they did? The booklet in the Perry's English set shows red crosses on all sorts of colours, usually a little cross-shaped bit of fabric stiched on.The French supposedly wore a white cross in the same way, and continued to do so for the rest of the century and beyond. However I think even more so than the English, there was never any uniform colour it was worn over. Later it seems different companies might have had their own livery colours, probably decided by their commander, or town if they were an urban militia... So you might see the white cross over various other colours.As for the Burgundians, they did adopt the diagonal cross ('saltire') of St Andrew later on, I personally don't know if they had done so at this stage though? Certainly during the time of Charles the Bold, many decades later, they were using it prominently, and it remained an important symbol of 'Burgundy', and thus was used by the Hapsburgs (who essentially inherited the Burgundies territories after the death of Charles the Bold), and so later founds its way to becoming a Spanish symbol....Personal livery colours of nobles' retinues were a thing, and are the subject of much study when you look at the Wars of the Roses in England. How widespread they were among the French at this time, I could not say.My personal way of approaching it would be to paint them all in random colours, with an informal scattering of the appropriate crosses for the French, English and possibly Burgundians. But that's just my personal taste - I don't like things looking too uniform for this era.The Perry booklets do show how the clothing of the French and English men-at-arms / knights did differ a bit - basically the English preferred their armour uncovered, whereas the French (and other Europeans) seemed to like a variety of somewhat outlandish coverings to their armour - sometimes, but certainly not always, displaying their heraldry if they had it. I imagine Burgundians and Flemish would be just the same in appearance as the French, and the 'lesser soldiers' of everyone would look much the same (with the exception that of course the English would be archers, whereas the Europeans would be more likely to be crossbowmen, spearmen, and others).If I ever did this period, I think it would be a great opportunity to forget about uniforms and have all units being a riot of different colours. Could be a fun change if you're used to the 19th century?
As for the Burgundians, they did adopt the diagonal cross ('saltire') of St Andrew later on, I personally don't know if they had done so at this stage though? Certainly during the time of Charles the Bold, many decades later, they were using it prominently
If I recall correctly, the Burgundians had adopted the (red) saltire by 1412, so should be fine if you are gaming the Agincourt to Orleans period or slightly before.