@Parzival
Thanks for the questions
1) – Yes indeed, they did. Think of the French in the late medieval period, and first thing you no doubt think of is them being mowed down by English longbowmen in the Hundred Years War, and comparisons between English longbowmen and French crossbowmen.
A few points to consider:
- The Hundred Years War ended in 1453 – so another 47 years of French military in the 'medieval period', if you want to consider that ending at the year 1500! My French are from the 1470s and 1480s.
- The famous battle of Agincourt was in 1415 – so there's 38 more years of the Hundred Years War for the French to adapt their military system. The did in the end win the war after all!
So yeah the French military changed a lot in the final years of the HYW – new attempts at a permanent military force ('compagnies d'ordonnance') loyal to the crown, adapting new tactics learned from their earlier defeats against the English, a growing use of gunpowder weapons (mostly artillery but also hand-held guns)… and yes, attempts to raise large forces of longbowmen to rival the English. It's worth noting that in the latter decades of the HYW the aren't any examples of English archers winning battles.
So by the time we get to the latter half of the century, both French and Burgundian armies did indeed use large numbers of archers. The ordonnance companies of both French and Burgundian armies had 2 or more archers for every mounted man-at-arms.
Longbowmen weren't some sort of 'super-soldiers', but they were considered important for the military tactics of the day, at least in France, Burgundy and of course England.
2) – The white cross of St Denis was adopted by the French during the HYW, and continued to be used for years/centuries to come. There wasn't anything like a national 'uniform' in this era, and the white cross would be used on top of any colour. There's a vague idea that red was the most common, but I honestly don't know how true it is. Still, I went for red for most of my French units! You certainly see a white cross on a red background on a lot of French flags and liveries in period artwork. National uniforms may not have been a thing, but 'liveries' were, and different French companies/units/etc would have worn some sort of livery, presumably featuring the white cross. Quite how uniform/smart the liveries were, and how common red was… who knows? (I do have some other French units in different coloured liveries, but all with the white cross)