When I click on the FO3 desktop icon , a small screen pops up saying that FO3 isn't compatible with my windows(10) version and that there's probably an update available . When I close down that pop up and click on the play button , the screen goes purple and the game crashes . So , how to solve this ?

Go to Document\My Games\Fallout 3 folder, open the .ini file, and set the value of "bUseThreadedAI" to "1"
Then just below it, copy and paste this: "iNumHWThreads=2" (if it crashes change the value to "1")

Run the game as an administrator and in Windows XP SP2 compatibility mode.

Download and install FOSE (http://fose.silverlock.org/) also as an admin and in Windows XP SP2 compatibility mode.

If it still crashes, download and extract this mod (http://www.nexusmods.com/newvegas/mods/53635/?). To install it, symple extract "nvac.dll" from the "NVSE\Plugins" folder, in the FOSE\Plugins folder.

Source:https://www.reddit.com/r/Fallout/comments/3lvoh0/windows_10_states_fallout_3_isnt_compatible_how/cv9ytmv/

Also don't forget to run the Fallout 3 Launcher first if there is no .ini file in the Documents\Fallout 3 folder.

Good luck!