It's possible, easy, but time-consuming if you want to change it for every archer unit there is.
In the folder AotR is installed, find this file:
\data\ini\weapon.ini
Open it with a text-editor, then find the weapon of the archer you want (Ctrl+F should let you search, in most cases).
Now, finding the ones you want to change can be a challenge, if you're not familiar with coding BFME, and even if you are. You see, There's over 2000 references to either AttackRange (a good thing to search for), which is the value that determines the attack range, which makes it take quite a while. AttackRange applies to all ranged weapons, so you'll have to sift through archers, spear-throwers, catapults and ranged magical abilites, and probably some I forget. It's tedious, to say the least, but quite possible. If you just want to play around with your favourite faction, you can search for the name of the units you want (ie., MirkwoodRanger), or logical clues like bow or archer. If you want to adjust all of them, searching AttackRange and changing them as you go is probably best. You can technically look through the entire file manually, but I think it's around 60-70k lines of code, so it will probably take a while...
If we use an example:
MirkwoodRangerBow has the range of exactly ELVEN_LORIENARCHER_ARCHER_RANGE. You can simply replace ELVEN_LORIENARCHER_ARCHER_RANGE with any number. However, if you want to know what the range actually is original (ie., what ELVEN_LORIENARCHER_ARCHER_RANGE is), you'll have to find it in either \data\ini\gamedata.ini (or \data\ini\default\water.ini). In gamedata.ini you can search for ELVEN_LORIENARCHER_ARCHER_RANGE and find that it's set to 350, so if you set the AttackRange in weapon.ini to 700 you know that it'll be twice the range. Don't change anything in gamedata.ini itself, that file is one of few that won't be read by the game when you play the mod, so any changes are ignored. Any changes you make to weapon.ini will work, however. So, you can safely set the AttackRange = 700, or any number of your choice.
I'd recommend making a copy of your installed AotR folder so you have a backup without having to redownload.