I would say that you're never required to renew a visa, you're required to either have some title to stay or leave. Usually, you want to renew the visa but in that case it would seem unnecessary as staying as an EU citizen is generally simpler and more beneficial.
One common situation in which you let a visa expire and nothing happens is if you gained French citizenship in the meantime. That's common, they know how to handle it. In theory, I think you are supposed to surrender your carte de séjour but I know some people who could hold onto it. Of course being French also comes with more fundamental changes to your relationship with the French state so it's not exactly comparable. And, in practical terms, one major differences is that the préfecture will not learn about your new citizenship automatically.
Still, I think the absolute worse that could happen is that you receive an obligation de quitter le territoire français a few months after the expiry of your current visa/residence permit at which point you can still send a letter pointing out their mistake. Your rights as EU citizen are very strong and cannot possibly be denied because of some procedural details. To forego the whole unpleasantness, I would probably send them a letter informing them about the change and apply for a carte de séjour EU (which is not mandatory but is completely free) as soon as possible. That way hopefully someone at the préfecture will notice before they make their periodical sweep through the files to find potential overstayers and it would at least provide you with a paper trail if any question arises.
At the same time, I can't see why your visa would cease to be valid or you would be legally forced to switch to another status so you could in theory go for a renewal, I guess. But of course doing so would probably create some surprise and confusion if the préfecture learns about your new citizenship.