The two answers so far have differing advice. Could Cécile comment please?
Laura Lawless’s explanation seems to accord with Alan’s - se parler is one of "20 verbs for which the reflexive pronoun is always an indirect object" (That is, they’re talking to each other, not talking each other, and parlé is invariable.)
https://www.lawlessfrench.com/grammar/agreement-with-pronominal-verbs/