In a nutshell, I'm debating starting up a campaign that would use the Hundred Years' War as a backdrop, and as such, would have many battles that would have hundreds or thousands of combatants. Is there a way to simulate such interactions?
Only unreleased playtest rules right now
There are no officially-released rules currently for mass combat in 5e. However, they do have playtest rules available for mass combat released under Unearthed Arcana. That is available here. Also an older set of UA rules regarding mass combat here.
Note that all Unearthed Arcana is going to be much more rough around the edges and likely to have errors, rules holes, or imbalances than the officially released rules. So tread carefully. At the very least, it should be a good place to start.