For a while now, Fallout 3 has become nigh unplayable to me, even with FOSE, the game is constantly hard freezing randomly, forcing me to Alt-Tab to close the game, I have started a new game multiple times and it's still hard freezing. I assume it has to do with my Mods' loading order but I don't know how to organize them in the correct order.

The fact that it hard freezes while paused and in Pip-Boy pause shows that the problem is more complex than I thought.

You can try to look on internet for the crashes, there are a lot of problems and workarounds
But you should send us the load order just to see if you did install useful mods for performance
However for the Load Order you can use LOOT : https://loot.github.io/

It is a software that will automatically sort your Load Order
You can look on the website for the readme https://loot.github.io/docs/0.9.2/LOOT%20Readme.html

And btw I recommend you to use Tale of Two Wastelands if you own New Vegas, it's basically Fallout 3 (and NV) running on New Vegas engine, so you can use most of New Vegas mods and you have features like Ironsight and other things that Fallout 3 doesn't have compared to New Vegas

You would need to share your mod list for more useful input.

If you haven't already, I'd suggest including the following for overall stability.

Updated Unofficial Patch
lStewieAl's Tweaks
NVAC
OneTweak

This might be a more difficult solution, but you could try running "A Tale of Two Wastelands" (a.k.a. TTW). It uses the more stable Fallout:New Vegas engine to run both that and Fallout 3. If you follow their install instructions exactly, it should be stable. Besides the multi-step install process which, though well-documented, can be laborious, there are some issues with (poorly written) mods and certain tools. It's all laid out on the website...

Google "A Tale of Two Wastelands" for details.

New Vegas really isn't any more stable inherently. Both it and FO3 can be made stable with effort and mods though.

I think I found the solution to my problem, I think.

It was the Unofficial Patch, since the new versions ask you to extract all of its data into your Data Folder through the Mod Manager or the Mod Organizer.

I was using files from an old UF3P version while using a newer version of the patch.

The thing is that old UF3P versions came with an installer and the .bsa file while the newer ones simply come with a .bsa file and ask you to extract all of its files manually before using.