If Frederic Jacobs says he communicated with Schnorr, then that's what happened.

If Frederic Jacobs says he communicated with Schnorr, he thinks he communicated with Schnorr. It's possible that someone is impersonating Schnorr.

If only there was some kind of way of proving who you were... possibly using public key cryptography? ;)

Elliptic Curve Cryptography still has an excellent theoretical security record, and will likely keep its record until the advent of quantum computers. Also, trustworthy digital signature is actually not too difficult even given the doomsday scenario - if all public-key cryptosystems are broken, as long as you still have a secure hash function, you can use Merkle signature [0].

[0] https://en.wikipedia.org/wiki/Merkle_signature_scheme

This only works for alice and bob.

This is mildly important. It's someone that claims to have communicated with Schnorr.