This is the long-barrel, long-grip version of the FN Model 1910. It was introduced in 1922, so it is usually called the Model 1922 or Model 1910/22. Yours has the wood grips used on pistols made for the Germans some time after they conquered Belgium in May of 1940. FN may have continued to use these grips on guns made after the Herstal factory was liberated in 1944, and even for a while after VE Day (May 8, 1945). Of course, it is very easy to swap grips between pistols, so they may only be on this gun because a previous owner liked them.
Guns made for Germany would have German official acceptance marks, usually called "Waffenamt numbers". These marks included a simplified German eagle. A Waffenamt number was assigned to an individual, so the numbers used on these pistols changed several times during the war. This can help identify when the gun was made. However, I don't know where to look for them on the Model 1922, and I cannot spot any in your pictures.
There seems to be a lot known about the serial numbers and markings of these guns, and someone here probably either knows it or can tell you where to find it. This post in a different forum suggests some of what is known:
https://www.milsurps.com/showthread.php?t=69784 The pistol in it also shows the broad-nosed trigger that mid- and late-war German occupation 1922's had, but is too blurry to show Waffenamts.
To me, the interesting thing about your gun is the odd machined cut above the extractor in your 3rd photo:
https://www.thehighroad.org/index.php?attachments/20230124_073220-jpg.1129149/
I can't recall seeing that before, and a quick (emphasis on quick) Google image search does not show any other Model 1922's with it. If it was done by the factory, it would probably increase collector interest and therefore value.
As to value, I am sorry, but I don't know anything about gun prices any more, and with a pistol like this, it can depend on fine details like which particular Waffenamt number it has and so on. If you register with GunBroker, an online auction website, you can use the Advanced Search functions to check the "Completed" auction listings for similar guns. I will say people seem to ask very high prices for WWII German weapons now, but I have no idea if they get them. (I should also repeat that I am not certain your gun was made during the war.)
One more thing - the holster with your gun is for a Russian Makarov pistol, and is the style used by the Warsaw Pact armies in 1991, when the Soviet Union collapsed. It is useful, but has nothing to do with FN Model 1922's.
PS - The second photograph here:
https://historical.ha.com/itm/handg...del-1922-semi-automatic-pistol/a/6177-40620.s shows the German acceptance stamps, although they are a bit faint. I am sorry to use an auction link, but I could not find another good example quickly.