It's equivalent mostly in terms of cultural significance (historical university etc..) . It's still one of the best university in France in terms of reputation and name recognition for a "university". Grandes écoles form a parallel track that gathers the best students due to a very selective and tough entrance process (2 years of intense preparation). Universities can still have great programs and do great research (and really smart students who didn't want to do the Prépa), but there is a certain little extra for having gone to a grande école.

Now, apart from some programs at specific universities, there is not much difference in universities in France at undergraduate level, acceptance is high because getting the French baccalaureate (high school diploma) guarantees access to universities. With the new system it might not be your first choice program, though before that meant basically a 100% acceptance rate at undergraduate level (this needs to be updated). Selection happens throughout the course as people drop out or fail exams. The stats were quite telling before.

Also, because there is not much difference between unis, people tend to go to whatever was closest to home for undergraduate studies.

When it comes to elitism and "excellence", the Oxford equivalent would likely be the ENS Ulm, at least for the 20th century. Sartre, Derrida, Foucault, de Beauvoir, etc, all come from there.