Facebook not compatible on Android 4.3
You could try installing an APK manually.


Go to Settings &rarr; Security and enable installation of apps from unknown sources. 
Visit APKMirror and click the blue download button. Once the download finishes, click the notification and install the app.


If that doesn't work, you could try the above process again with Facebook Lite, although it looks significantly worse, and may or may not work properly (possibly depending on the country you're living in).

After you've finished installing APKs, you should disable installing apps from unknown sources. 


Go to Settings &rarr; Security and disable installation of apps from unknown sources -- this is important to do, because else you could be tricked into installing a malicious app.