A few small, scattered, out of context, highly mutated facets of Roman culture have survived here and there. None of these, except Christianity, were among those most important to Romans, or those they saw as primarily distinguishing them from other cultures.

And RC Christianity, apart from the name, is vastly different today than in 500 CE (and both are vastly different from RC Christianity in, say, 1300 CE). A modern Catholic would certainly be considered a sinner and a heretic many times over in 500 CE, and probably vice versa as well (I haven't checked).

Incidentally, we are corresponding in a language that has much more in common with old Germanic tongues than with Latin, but it doesn't follow that we retain any of their culture. And here in Israel I talk and write a Hebrew which is quite similar to late Roman-era Hebrew - certainly more so than English is to German or Latin - and Orthodox Jews are the biggest religious segment in the country, but it doesn't follow that we (the non-religious people) have anything in common with ancient Jewish culture. (Consider that the vast majority of Europeans don't strictly follow RC rules either.)