False Appearance is not being hidden
Hidden means "both unseen and unheard" (p. 194 PHB). False Appearance does not make the monster unseen and unheard, it just makes it look like something else. Here is an example False Appearance entry from the Roper:
False Appearance. While the roper remains motionless, it is indistinguishable from a normal cave formation, such as a stalagmite.
You can see the stalagtite clearly. You just don't realize it is a roper. It is not hidden. If the monster wants to be hidden, it needs to follow the normal rules for hiding from the Basic Rules:
When you try to hide, make a Dexterity (Stealth) check. [...] You can’t hide from a creature that can see you clearly, and you give away your position if you make noise, [...]. An invisible creature can always try to hide. Signs of its passage might still be noticed, and it does have to stay quiet.
Hiding: If the characters are temporarily blinded, the monster is invisible to them and can attempt to hide in plain sight. It needs to succeed on a Dexterity (Stealth) check to do so. If it does, it can also use that check to move to another space quitely and without leaving tracks. Without a check or if it fails, the characters will hear if it moves to another space, and know where it moved to.
False Appareance: The monster also can use False Appearance to appear as whatever terrain feature it looks like, without needing to make any check. While the characters are a blind, they will not see the transformation.
Once the characters' blindness wears off, if there was nothing to hide behind, they will see the monster, and it will lose its hidden status because you cannot hide from a creature that can see you clearly. Their vision is not obsucred in any way, they can see the monster clearly, it just does appear to be something else, so that is true, wether the monster is using False Appearance or not.
Will the characters realize what is going on?
So if the monster did use False Appearance, the question then is if the characters (and players) will realize that the terrain feature they now see is the monster. This will is up to the players, you just describe what they see. They than decide if and where they want to attack.
If the monster did not move, they heard no movement and now there is whatever it appears as in the space where the monster used to be.
If the monster did move and failed or did not make a Stealth check, now there is whatever it appears as in the space where the characters heard the monster move to.
If the monster did move and made its Stealth check, they heard no movement and now there is whatever it appears as somewhere in the vicinity. Depending on the rest of the environment, this may be obvious or hard to recognize: empty room without features - obvious. Room full of stalagmites with one extra stalagmite somehwere - hard, and likely worthy of an Intelligence check or similar to see if someone can pinpoint it, if they try to.
Special False Appearance
There is an extra wrinkle in that some kinds of False Appearance can make the monster appear as if there is no object there at all. Here is an example from the Trapper in Volo's Guide to Monsters:
False Appearance. While the trapper is attached to a ceiling,
floor, or wall and remains motionless, it is almost indistinguishable
from an ordinary section of ceiling, floor, or wall. A creature that can see it and succeeds on a DC 20 Intelligence (Investigation) or Intelligence (Nature) check can discern its presence.
In this case, if they know the space or not, they would not see anything unless they spend the effort to make an Intelligence check (which the DMs may rule to use their action for the turn). They might still attack the space where the monster was, or a space they heard to move it to, or a random space in the hopes of hitting it there. Or they might think it teleported away.