Is there a word used to describe a weekend plus a one-day holiday?

In English, this is commonly called a 'long weekend'. Depending on the length, 'three-day weekend' or 'four-day weekend' works as well.

In British English, a public holiday is called a "bank holiday", and when it occurs on a Monday, as it often does, the three-day period is called a "bank holiday weekend".

One more possibility is the phrase holiday weekend. From Merriam-Webster:

a weekend that is preceded or followed by a holiday

This is my go-to phrase in situations like you describe, since it doesn't assume that the other person actually gets the holiday off from work (I don't get MLK Day off, for example; rather, my employer offers events at work celebrating MLK, Jr.'s legacy).

So you could say something like:

How's your holiday weekend shaping up? Do you have Monday off?

It also works for slightly longer holidays, such as (the US) Thanksgiving, or the 4th of July when it falls on a Tuesday or Thursday.

I think we need to coin the phrase, Threekend