Really two ideas, the first rather mundane, the second i’m sure will be quite controversial.
Decrease the food cost of the militia line. Whether you adjust the cost directly or increase the effect of supplies, I don’t have a strong opinion on. Probably not more than 10 food cheaper. Maybe only 5 food cheaper.
Decrease the strength of the Knight slightly.
The knight is the primary point of comparison, and it’s just sooo much better. No upgrade cost whereas you need to upgrade MAA to LS and probably at least pick up supplies before it’s semi-viable. Knights dominate 1 on 1, have higher pierce armor, greater mobility, etc, etc.
If you decrease a knight’s hp by maybe 10, and make the Longsword a little cheaper, then perhaps it’d be competitive when resources are balanced. The knight would still have advantages, but then LS might be viable. Cavaliers could still have their 120. Perhaps that’d make knights too weak to camel civs, but you could balance by reducing the attack bonus of the camel rider. Leave the heavy camel rider just where it’s at. Pikes might be “too strong” then but the Knights don’t need to take that fight with their mobility.
Gambesons helps the militia line against crossbows, so I think the LS is doing ok with that matchup. They really just suck a lemon against knights, even when resources are balanced.
I think knights are generally considered to offer a huge power spike in castle age, so I think there’s a little room to take them down a notch without ruining the unit altogether.
I also realize then the Franks bonus of 20% more HP, would result in knights having only 108HP, compared to generic civs with bloodlines, having 110. Admittedly it’s still free, so not a bad bonus, but a less good bonus for sure.