Photos would help. The finger parquet floors had different thicknesses - back in the day. The "economical" versions where quite thin and almost impossible to refinish. The mid-range one's where just thick enough to get one good sand and refinish. The HIGH END parquet floors were as thick as solid hardwood and had multiple sand/refinish options because of it.

Without seeing photos, and without knowing the thickness of the product (you can find a floor vent that pops out so that you can measure the thickness of the parquet) I can't be sure which category your floor falls into.

If your floors can be refinished, that is the way to go. The average cost of a regular sand/refinish is between $4 - $5/sf. A parquet takes a bit more skill and a bit more time so it has slightly higher price range (like $5-$6/sf). That price SHOULD include a stain.

Many people are modernizing their parquet by using a DARK stain. Jacobean or even Ebony are being used to get these old orange floors to look sharp/hot/modern. And it works...beautifully.

Compare the price above ($6/sf would be a good benchmark) with a hardwood floor. A lower grade hardwood STARTS at $6/sf...and then you have cost of install. For me, those old parquet floors are really cool. Not everyone has them...but almost everyone and their DOG has a low-end engineered hardwood or laminate that looks like hardwood.

If this floor can be refinished, that would be my first choice. Look at the darker stains - especially for Red Oak (I'm not fond of Red Oak in a clear coat...it has too much cinnamon/peach in it for my tastes).

Please post photos...that helps a lot.

Photos, please.

Parquet really has no "era" ...

Yes, pictures if you can.

I agree that parquet can be timeless..all depends on what parquet you have.

Parquet can look great if finished natural, with the color removed or given a white treatment of some sort. You can get a bright and modern-looking end result.

Nice floor jfc. Absolutely modern.

Hmmmm...OP seems to have disappeared. Oh well. We tried.