Ricus and riccus show up in late Medieval and Humanist Latin, but they're certainly backports from French and Italian, not pre-Medieval loans. The various Romance cognates of rich are actually believed to represent three separate borrowings from three separate Germanic languages:
Italian ricco is the most telling one, because it has a geminated consonant, suggesting that its etymon went through the High German consonant shift, part of which involved intervocalic /k/ becoming /xː/: "Proto-West Germanic" *rīkī > Old High German rīhhi /'riːxːi/. Early Italian, not having /x/, transformed that back into /k/, its closest equivalent, but kept the length.
Dating that shift is complicated—it might have started as early as the 3rd century CE—but we have a smoking gun in the Lombards, a Germanic people who spoke a High German language/dialect (Lombardic actually provides some of the earliest attested evidence for the High German consonant shift) and settled in Italy in the 6th century CE. Lombardic contributed a bunch of words to Italian, and this is one of them.
In all other Romance languages geminated consonants were reduced, so we can't really tell if Spanish/Portuguese rico reflects a geminate or not. However, if Spanish rico reflected an inherited Latin ric(c)us, it would be rigo instead: in the Iberian Romance, voiceless intervocalic consonants regularly became voiced. (The outcome of /k/, specifically, is actually complex, but barring learnéd restoration from Latin, I'm almost sure it should be /g/ here. And learnéd restoration seems unlikely, since the word isn't attested in Classical or early Medieval Latin—where would they restore it from?)
So it must be a late loan, and again we can turn to historical evidence: the East Germanic Visigoths conquered most of Spain in the late 5th century CE, and their kingdom persisted until the early 8th. Attested Gothic reikeis /ˈriːkiːs/ is a perfectly cromulent candidate for the etymon of rico, borrowed after the aforementioned sound change.
The history of French is complicated and messy and as far as I know it's certainly the case that French riche could reflect Latin rīc(c)a, but then it would probably be ric in the masculine (on the model of L siccus > F sec, L sicca > F sèche; /ʃ/ (earlier */tʃʲ/) is a regular development of /k/ before original /a/). I'm actually not sure why Frankish *rīkī would produce the [ʃ] (maybe the form borrowed was *rīkijā, and it wasn't borrowed very well; maybe someone else knows), but the general consensus seems to be that that is indeed its etymon.
The Franks, of course, interacted with the Gallo-Romans from the moment they came into existence until, well, today. (But so did any number of West and East Germans.)
In the Eastern Romance, finally, the word doesn't show up at all, and the usual word for 'rich' is bogat, borrowed from Slavic. That doesn't necessarily mean it never had a rīcus (modern Romanian *ric/rică?), but it at least doesn't disprove a lack of common heritage.
Finding ricus in Pompeii graffiti would be very exciting, but I don't think it's going to happen.