Having a sample of the plaintext allows performing a known-plaintext attack against the underlying cipher. Unfortunately for ransomware victims, the ciphers typically used by attackers, such as AES, are not vulnerable to known-plaintext attacks in any way that matters. If you cannot obtain the key, you're out of luck. You can only use this as a learning experience and keep more backups.
A known-plaintext attack involves an attacker (in this case, you) being given input/output pairs for an unknown key but being unable to feed arbitrary inputs (or outputs) into the cipher. This kind of attack is useful for performing linear cryptanalysis, a powerful attack that can break some ciphers. AES is not vulnerable to linear cryptanalysis. Even if you could adapt inputs arbitrarily based on the outputs, you could perform more powerful differential cryptanalysis, but AES is not vulnerable to that either.