I'm running a campaign at the moment and one of the characters got feeblemind-ed.

If another character used polymorph to change them into something with higher Intelligence and Charisma, would this work?

Yes

Assuming you are talking about the polymorph spell (other spells may vary but most will actually have the same effect).

The spell states:

The target's game statistics, including mental ability scores, are
replaced by the statistics of the chosen beast. It retains its
alignment and personality.

So if the target is polymorphed into something with higher mental ability scores then yes - they may end up smarter, wiser and/or more charismatic! At least until polymorph ends.

Note:

Some argue that this would not work because Feeblemind, being a higher-level spell, would override a standard Polymorph.

However, as Mindwin points out in his own answer, the rules about overlapping spell durations (which states only the most potent effect applies) would not apply here because Feeblemind is an instantaneous spell. Its effects may last a long time, but the actual spell itself is instant. Hence even a standard level casting of polymorph would temporarily override those effects.

Yes

Feeblemind is a instantaneous spell with a lasting effect that grants a save to remove.

On a failed save, the creature's Intelligence and Charisma scores become 1. [...]

At the end of every 30 days, the creature can repeat its saving throw against this spell. If it succeeds on its saving throw, the spell ends.

Instantaneous spells do their effect then end. Feeblemind won't keep a check on the INT and CHA scores to set them to 1 every turn. It sets those scores once, and then it is done. Save every 30 days to revert back.

Given this characteristic of instantaneous spells (they don't linger as a spell effect), anything that modifies either INT or CHA scores later will have their effect. Including polymorph. The save every 30 days would still be rolled.

No.

I would say that the 8th level Feeblemind would override the 4th level Polymorph.

A spell’s level is a general indicator of how powerful it is.

The rules only describe how the same spell can affect a target multiple times, but the logic seems sound for opposite effects.

The effects of different Spells add together while the durations of those Spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.

Also, Feeblemind describes specifically how to be ended.

The spell can also be ended by greater restoration, heal, or wish.

Polymorph is not an option.

I would only allow Polymorph to override Feeblemind if upcast with a level 8 or 9 slot.