I'm about to start a new campaign, so I'm looking for minor buffs to the fighter.
I think prof. bonus to damage is very simple and easy to remember. Added.
I'll do my standard bonus background for something "fightery" like soldier to help in social & exploration.
I think Consistent attack makes a lot of sense with the 5th level requirement.
Consider these replacement features.
Heroic Action
You can act tactically in the moment to change the course of a situation. At the end of your or another creature's turn, you can take an action as if it were your turn, with some restrictions. If you use the Attack Action, you can make one attack or use an ability that is used in place of one attack. The Cast a Spell Action, or special actions granted by other class features that normally use an action costs 2 Heroic Actions.
During another creature's turn, you can instead use an ability that normally requires a reaction without spending your reaction for the round.
You cannot use this ability during or at the end of a turn in which you use your reaction.
Finally, you can use this feature to push harder and get more out of a single action, instead of taking an additional action. After you roll an ability, but before you know the result of the ability check, you can use a Heroic Action to roll a d10, and add the result to the check. When you roll to deal damage to any target, you can use a Heroic Action to add a d10 to the damage roll.
You can do this 2 times, or a number of times equal to half your fighter level, rounded down, whichever is higher. You regain all uses of this feature when you finish a long rest. At level 17 you gain the ability to regain all your spent Heroic Actions by spending 1 minute catching your breath, and regain the ability to do so when you complete a long rest.
This ability replaces the Action Surge class feature.
Heroic Determination
When you fail an ability check or saving throw, you can choose to succeed instead. You can do this a number of times equal to your proficiency bonus, and regain all uses when you complete a long rest.
This feature replaces Indomitable.
design notes: These changes make the fighter capable of just gritting their teeth and pushing harder than others can, and just getting the damn job done. You lose attacks compared to Action Surge eventually, but gain a lot more versatility and freedom. Especially being able to use it to add a die to damage after rolling to hit, which will allow you to save it for crits, or for when you really need it. Very nice for Champions, while the "use 2 actions to cast a spell" function is really sweet for Eldritch Knights. Consider limiting it to cantrips, though, and giving the EK a level 7 boost that lets them cast leveled spells with it.
I considered using proficiency bonus for the number, but it lost way too much compared to action surge unless you also bring in the "minute breather" regain at a much lower level, and that added complexity feels more like a high level thing.
An alternate I'd consider is to give only the d10 die at level 2, and have the extra action usage come online at level 5, to reduce "dipping".
With Heroic Determination, we all know Indomitable sucks, and this again lets you just use it to succeed in a wider range of key situations, in a way no other class can duplicate.