So the launcher doesn't crash when you launch it, but it crashes once you try to download one of the free games you've claimed so you can play it?
Have you tried an uninstall/reinstall of the Epic Games Launcher? This shouldn't entail uninstall all of the games. When you reinstall, if you use the same directory for games, it ought to automatically recognize all previous installations. If you customized installations for individual games, you should be able to manually point the launcher to those, but I haven't done this myself. I strongly recommend learning how to use an advanced uninstall utility like Revo Uninstaller Pro. One of the best expenditures you can make for the Pro version, btw. Otherwise, you might have to manually go through and delete temp files from your appdata folders (in Local, LocalLow, or Roaming). There could be a corrupted file there causing issues. It's the only thing I use to uninstall programs. I don't want any leftovers. It's a perfectly clean uninstall of not just the app, but all data & folders associated with it, plus any registry key tweaks or entries it made.
https://www.revouninstaller.com/
I'd run a Disk Clean, too, because it couldn't hurt.