Hmmm... not sure where you heard this, but as a general rule, the more teeth there are in a saw blade, the finer the cut will be, meaning the edges of the cut will be cleaner, less splintering. So 80 teeth is a "Fine Cut" blade and would be BETTER than a standard crosscut blade, which typically have 40 teeth. But this technically IS actually still a "crosscut" blade. There are really just two types of blades in that regard, crosscut and "ripping" blades. Ripping blades have even FEWER teeth (16-24), because they are meant for hand-held or table saws where you are going to cut ALONG the grain and the higher tooth count would clog up with chips and dust, resulting in burning of the work. Crosscutting is going ACROSS the grain, either perpendicular or at an angle (miter). Within crosscutting blades there are various degrees of fineness in terms of the finish of the cut edges. But with the fineness comes more contact and more heat, so the higher the tooth count, the slower you can cut without burning the wood. The lower count crosscut blades then offer a faster cut, like when doing framing work and the higher tooth counts are for finish work where the looks will matter.
For parquet flooring, you WANT a high tooth count. A step above that are what are called "hollow ground" crosscut blades. They are made of better steel that is machined to be thinner toward the center of the blade so that less of the actual blade makes contact with the wood and deforms the cut edges. Blades with carbide tips will do the same thing because the tips of the teeth, the cutting surfaces, are slightly wider than the blade itself. With each of these improvements in cut quality, the cost goes up so you have to decide where to compromise between cost and performance. If this is a one-shot project, I would opt for the 80-100 tooth standard fine cut blade. But I've also noticed that carbide tipped blades have become so cheap that in many places that is all you can buy, and that's fine, they are good blades.