You really want to run the eCryptfs utility
It's basically a "fire and forget" script, you can tell it where your encrypted files are or it searches everywhere for them, then it asks for your login passphrase or mount passphrase, then mounts the files in "a temporary directory, in the form of /tmp/ecryptfs.XXXXXXXX" for you to read/copy.
[You can even see exactly what the shell script does if you're so interested with
less $(which ecryptfs-recover-private) ]
AFAIK the eCryptfs utilities have not been ported to windows, so you'll have to run a linux. Just about any distribution that supports eCryptfs should work, but Ubuntu 16.10 should still run good enough to just decrypt & read files even though it's no longer supported (16.04 is a LTS and still supported, or a more recent Ubuntu will probably read the older eCryptfs files ok).
Boot a live linux ISO and work from there, copying decrypted files to another windows-readable format/drive (or windows readable encryption if desired, TrueCrypt-like, VeraCrypt, maybe even LUKS?).
Booting from a USB or DVD is easy, or even from hard drive file if you repair or recover the bootloader (grub?) - actually running Boot-Repair from a live linux might get your old Ubuntu bootable again, but there's a chicken-or-egg problem booting another linux first anyway.
Use a virtual PC (like VirtualBox) to run a linux ISO, directly reading and decrypting the encrypted files (or if they're relatively small then copying them into the virtual linux PC).
Your folder descriptions sound a little off, there should be a
/home/user folder with very little contents, and the
/home/.ecryptfs/user folder with the actual encrypted contents, but that shouldn't be important unless your encrypted files have been deleted somehow. The recover script does a good job searching & should work if they're still available.