Ah I saw your thread on this subject over at TMP, let's see if you can get some advice here!
Do you have any pics?
Are these Perry Miniatures? From your descriptions it looks like they might be.
Their Agincourt To Orleans range covers the 1415-1429 period of the Hundred Years War. Does it look familiar?
https://www.perry-miniatures.com/index.php?cPath=23_36&osCsid=qau0m83loquhkdgab48hve0jh3The mercenaries, knights and light cavalry on sprues you mention sound like they are from their Wars Of The Roses range, which covers a later period (roughly 1450-1500) and has noticeably different styles of weapons and armour.
So it sounds to me like you have two armies for the Agincourt period (french and english) plus some unassembled WOTR kits.
If you are new to medieval gaming, what periods do you already play, and what sort of scale game (mass battle or skirmish)?
Lion Rampant is apparently a popular ruleset for fast-paced, light-hearted games. You have more than enough models for it.
If you want a bigger battle experience, you should consider looking at Hail Caesar, or maybe To The Strongest. You will obviously want to get movement trays to group the individual bases on for these games.
As has been said, actual 'siege' games would be a rather dull affair, but smaller skirmishes and such as part of a larger siege campaign would be great. Assaulting a breach in the walls, sallying forth to surprise the besiegers, ambushing reinforcements on the road, trying to capture the siege engines (which in this period would be large 'bombard' cannons)...
Anyway, looks like you've got too good sized armies there. If you wanted to expand them, it never hurts to give the English more longbowmen.