It's worth remembering that the Romans didn't have a 7-day week Their nundinae was 8 days long, the seven day week was middle-Eastern in origin and began to appear during the early Imperial period, primarily from Jewish and Christian sources.
As far as I can tell, the Republican Romans did not name the days of the week or assign religious significance to them. Up to the point where Caesar reformed the calendar in 46BC, it was theoretically a lunar calendar -- I will avoid the glorious detail, but you can find good summaries on Wikipedia at Julian calendar and Week -- but was close to chaotic due to political manipulation and inaction.
Days were referred to as "x days before the [Ides, Nones, Kalends] of March". Holidays were tied to the annual calendar and work days were ordered by an essentially arbitrary scheme. It did not repeat on either a 7-day or 8-day cycle.
While the 7-day week was known as early as 100AD -- Plutarch is known to have written a book on the subject of why the days of the week are named as they are around then, but the book is lost -- Rome did not move officially to a 7-day week until 321 AD when Constantine officially decreed a seven-day week in the Roman Empire, including making Sunday a public holiday. (There was a very complicated system of days being designated with one of seven designation to say what could be done by the Republic on that day: Courts open, public assemblies possible, filing of lawsuits possible, etc.) ((One sometimes wonder how Rome conquered an empire when it couldn't manage its calendar...))
There is graffiti from Pompeii mentioning a day of the Sun, but, interestingly, it seems to have been a different day or the week than other attested days of the Sun. (Since the week was not very important, it's possible that different areas used different 7-day weeks right along side the common 8-day nundinae!)
The Wikipedia article on the Roman Calendar may be useful.
As the Empire went on, the 7-day week gained in importance but at the same time the classical pagan religion lost importance: Long before the triumph of Christianity, Rome had faced the reality that its traditional religion provided little or no emotional or spiritual help for people who were increasingly adopting beliefs that did. The period of the 200s and 300s featured a fascinating attempt by philosophers -- the Greek/Egyptian Plotinus is best known -- to create a synthesis of the classical paganism with Platonic philosophy. (Some of the more interesting intellectual documents from that era were debates between Christians and Neoplatonists.)
Of course strange Eastern customs came to Rome. e.g., Juvenal around 120AD: "Syrian Orontes has long since flowed into the Tiber, and brought with it its language, morals, and the crooked harps with the flute-player, and its national tambourines, and girls made to stand for hire at the Circus." Who knows if he didn't also have a 7-day week in mind?
Bottom line:
- Republican Rome did not use the 7-day week and didn't for the most part organize their calendar that way.
- In later Imperial Rome even the non-Christians and non-Jews would probably not have fooled around with the old pagan gods other than in public rituals.
- It is very unlikely that eating fish on Friday for Venus was a common or general practice at any time.
- Rome was big and Rome was full of people of all nationalities and all sorts and, especially in the 1st century might have had Romans adhering to an Oriental cult which ate fish for Aphrodite.
- But I can't say I've ever heard about it.
There. A nice clear, decisive answer.
