The Vernacular had shifted from classical Latin noticeably by 50 BC. 813 was well after the shift was on its way. The main features found in all romance languages (au -> o, us -> o, removal of neuter tense) can be seen on graffiti and a couple of individuals' names by this point. I think the next noticeable changes is the words used for yes (si, oc, oui) and the use of S for plural vs. the i/e thing in Italian.
Local languages did have an impact too, but I agree it was relatively minor. French does some weird Gallic thing for counting and probably has some German or Celtic words, Spanish eventually added some Arabic words. That's really about it, though.
Now I'm not saying that the language didn't change - just that's when the vernaculars were mutually unintelligible with classical Latin. That's what Xanikk's question was - when the divergence was far enough that there was mutual unintelligibly.
(as for mutual unintelligible romance languages today, some languages are still mutually intelligible!)