Facebook not compatible on Android 4.3

Well the app simply is not compatible with your device, I don't see direct fix for that but as workarounds there might be couple of tries.

1. Download older version which is the latest version that supports the phone in question. Disable the auto updating if you went with this approach. Problem with this approach that you'll have to find older version apk source, but such APK sources are not official usually, so beware and use the APK carefully.

2. Use normal browser like google chrome and bookmark the facebook page as icon in home screen like application. In chrome this could be done by opening the menu on any loaded page and clicking on "Add to home screen".

Notice that the second approach that I recommend and got some advantages over the app anyway. For example,

• Using the browser is much less power wasting compared to the app due my experience.
• Also the browser is the full site so all features and options are there specially the new ones immediately when they're added.
• Also, I need sometime to see the site like desktop user's view and that it possible via chrome and some other browsers as well like firefox and UC. Even built in browsers support such features.
• As disadvantage (noted by @iBug), a browser uses more data on cellular so more fees. Although I never experienced this and I browse facebook a lot but it makes sense.

You could try installing an APK manually.

1. Go to Settings → Security and enable installation of apps from unknown sources.

2. 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 → 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.