Devastating Strike
If you only make one attack on a turn, deal +[W] damage for each Extra Attack you have.
I'm using the 4e parlance for simplicity. Basically, if the fighter could make 3 attacks with a longbow normally, they could instead make a single attack for 3d8 damage.
This isn't something a fighter would typically use on their turn, since making 3 attacks is usually better. However, it would make readied attacks and OAs significantly more threatening. Currently, a high level fighter's OAs deal a fairly insignificant amount of damage, and having to ready an action results in an unreasonably large loss of damage, IMO.
Longshot
Every X levels, increase the close range of ranged attacks you make by 5, and the long range by 10.
I don't like that a 1st level wizard with 8 strength can throw a javelin or shoot an arrow the same distance as a (supposedly master of weapons) 20th level fighter with 20 strength. Sure, the fighter is far more likely to hit with the attack, but it still doesn't make sense that both attacks travel the same distance. This also improves the strength based fighter's innately poor ability to fight at range.
Historical Research
Once per X levels, the fighter player can declare they have tracked down a lead on a magical item chosen from [list of options]. The DM may choose to create and run an adventure, which should generally not exceed one session in length, after the completion of which the fighter obtains that item. Alternately, the DM may simply choose to have the adventure take place during downtime, in which case the fighter obtains the item after the downtime completes.
I believe that martial characters have a higher reliance on magic items than casters. Magic items are the domain of the DM, so their quantity and quality cannot be readily assumed. This creates a player facing option for obtaining a small number of curated items, enhancing the player's ability to create their fighter the way they envision.
I realize this thread stipulated nothing inherently magical, but this isn't. Anyone can technically track down a lead on a magic item and go on an adventure to retrieve it, assuming the DM allows it. This simply guarantees that the fighter can do so a limited number of times per campaign, without having to rely on fiat. The wizard is able to conduct magical research in the background while adventuring, so why can't the fighter research the location of magic items? The reason it may or may not require the actual adventure to be played out is because, from what I've gathered, some DMs take issue if magic items are "unearned", while other DMs may feel put out if they need to design an adventure specifically for this purpose. Hence, choices.