You may be able to buff out the scratches with floor wax if the floor is real wood.

DO NOT put any wax on your floor! Call a professional to look at your issue.

Get silicon glides for your chairs.

The parquet floors are real wood.

Any recs for the silicone glides? Will try and look on Amazon. TY

Were the floors finished for you? Do you know what finish was used?

It's most likely a urethane finish. Scuffs are essentially scratches and cannot be "buffed out". Light colored scratches can be improved in appearance with a marker pen but it doesn't restore the finish. Only an additional coat can fix that and it's generally hard to do for spot touchups, though your floor pattern would make it more feasible. It can also be tricky matching the sheen level when doing a touchup.

You might be able to use regular felt pads, cut to fit. Lightly sanding the foot first and applying a thin coat of contact cement will usually help the pad stick to small feet but when you consider that all the wear is taken up by a tiny little pad, it's clear that they're not going to last very long.

I wish I had a better solution for you.

There are three things going on here:

1. Scuffing = when foreign matter is ADDED to the finish (like black marks made by black soled shoes...or white marks put down by white soled shoes...etc). Rubberized sockettes can do this.

2. Scratches = when slight amounts of the finish has been removed or the finish has been 'broken through' (but not to the wood). Raw wood feet sliding on the surface can do this.

3. 'Buffing' or 'etching' = when a soft material is slid across the surface of the finish and it CHANGES the SHEEN/gloss level. Buffing makes it shinier...etching makes it duller.

You have all three events happening here. Thankfully you do NOT have any real damage. The finish looks to be in good shape. The finish is doing what it is supposed to be doing = take all the damage and abuse so the WOOD below is saved. That's why all wood finishes have to be refinished every once in a while....'cause the finish has been worn down by life. It happens every 25 years or so.

What can you do? The easiest thing imaginable....Nothing. Yah. Your best thing to do is nothing. Leave it be. It is fine. It is healthy. It is normal. The finish is doing the job it was meant to do.

Another option: area rugs. Yes. Rugs underneath those DASTARDLY feet (those are wood floor killers BTW...nothing you can do but live with it or get new furniture with different feet) will stop all of this. All of it.

The next next best option: A tennis ball can be used to 'buff out' the scuffs (it actually removes any 'foreign material' left behind. The scratchy surface of the tennis ball also BUFFS the floor (you will need to be on your hands and knees scrubbing back and forth so hard your vision begins to fade) to the higher gloss you are used to (win-win for the tennis ball technique)!

Anything that is 'left' is etching or minor scratches. And unless you have an extra $3/sf kicking around to have a buff and coat done over the entire floor (you are welcome to do this...but it will fix it for 10 days...and then the dastardly feet will do this all over again), you will have done everything possible to get your floors looking nice.

And please start working with a hot-glue gun and thick felt pads that do NOT have a sticky backing. You can hot-glue the felt to the feet to give you twice the amount of life. But they will still fall off.

I'm sorry but the feet of the furniture are causing all of these issues. The pounds per square inch are just too high (tiny feet = BIG load).

@SJ McCarthy, thank you. I agree, it's the type of feet on those chairs. I have 2 of them. My other side chairs have wider feet and the "socks" and those floor areas seem better. I'm getting silicone covers for now.