Although a lot of the things that I would like to see in a new FE game have already been said, I have come up with some ideas that have hopefully not been used yet (sorry if it has):
A class that uses the slingshot and a class that uses the boomerang
There are not very many classes in the FE games that have long range physical weapons, except for the archers, and there are few of them as it is. To have classes that used different long range weapons could add a twist in the gameplay, for it could be used to set up another weapon triangle between the bow, the slingshot, and the boomerang. Then the slingshot could be good at piercing armor and the boomerang could be great at taking down mounted units, both dealing bonus damage.
A class that combines archer and mage
I came up with a class called Spirit Arhcer, although it would function just like a regular archer until promoted. It would then become a Spirit Seeker, able to combine the might of bows with the might of any type of magic. As an example, let's say the Spirit Seeker had 17 Str and 13 Mag (they would have a higher magic growth rate than normal), and let's say the enemy has 10 Def and 4 Res. To figure out how much damage the Spirit Seeker would do, you would average their Str and Mag points, and then average the bow and magic they use. Let's say they are using an Iron Fire (Iron Bow and a Fire tome, forged perhaps). The might of the bow is 6 and the might of the fire is 5 (from Blazing Sword), rounding down to a 5 in might combined. The Str and Mag of the Spirit Seeker averaged together is 15, and +5 because of the weapon might =20. Then the enemy's Def and Res are averaged to 7, and there you have it.
20-7=13, the damage you would do. It is somewhat complicated, but then it would not matter whether the enemy had high Def or Res, for one or the other would likely be lower, and therefore give the Spirit Seeker an advantage.
(I hope that made sense!)