You may be able to have he floor refinished to a lignter shade but it will be expensive and it will still be a parquet floor next to tile.
Update parquet flooring.
If only a few of the pieces are damaged pry them out and replace them with a new tile.
Stain and seal parquet flooring to ensure that your floor is looking good for as long as possible simply wipe it regularly with a soft damp mop.
The run of the mill parquet flooring often found in 1960s and 1970s apartment buildings is not what today s buyers usually want.
I think the scale of the tile makes the parquet look tiny and busy.
Most people nowadays are leaning more toward plank hardwood.
A foolproof way to bring parquet floors up to date is to strip and stain them a rich dark walnut.
The first step will be to identify which all pieces are damaged and requires replacement.
Would you consider sanding it down and painting it.
You can purchase a ready tinted sealer in various colours or purchase a clear sealer and mix in your own stain.
Also in the mix are the creative efforts of the family run uk based parquet company mckay flooring ltd who are doing fun things like delineating different areas of a room by mixing ceramic and wooden parquet tiles on the same floor and updating traditional herringbone parquet by using different colored or painted blocks.
Dark wood floors always create a sense of luxury in a space and your idea to add area rugs is great for injecting interest and contrast.