It is very probably not the utmost that can be done nor a sure means in all cases, but the use of a dictionary such as the TLFi provides some indications such as « vieux », « rare », « archaïque », « régional », and those tell you that the word is not used much. Other indications, such as « familier » and « popular » tell you that it is used rather a lot.
I really don’t know of any means of getting a finer appreciation of the importance of the usage of a word.

Studies tell the average number of words routinely used by most French speaking persons is between 2000 and 5000, with a core of around 600 words, the ones required to be able to have a conversation.

I guess the number of words known is 10 times larger, i.e. someone using 3000 words would probably understand 30000 words. That’s still a rough estimation, individual variations would strongly apply.

Verbal forms, singular/plural, masculine/feminine variants are not counted in these figures and would increase them significantly.

There are also many rare or even non existing words people would understand simply by analyzing how they are built.

You can use the Lexique database to get a list of 142k French words with their lemmas (~47k) and usage frequency.

I agree frequency is not necessarily in a strict linear relationship with knowledge, but there is no doubt it is strongly related. Every adult French native speaker will know 100% of the 600 most used words, and a few percent or less of the words ranking 100k or +. On the other hand, browsing the lemmas ordered by frequency, I’m surprised to see the rank of a few of them, for example fuligineux is #17000 but I doubt many people know precisely what it is about while grisé is #28000 but understandable by most kids.

You suggested one word, étrennes in comments. Its lemma ranking is #18420 according to the Lexique metrics (17223 for the verb étrenner) so according to my rough range, it should be known by almost everyone even in the less literate group.

Instead of using the lemma frequency, you might also have a look to the Megalex data which measure words recognition time, both visually or auditory. According to it, almost all of the participants had a recognition rate better than 80% so that would mean they know at least 37000 lemmas. The study is presented in this page.

You need to pin down precisely what you want to know and what use you will put it to. The chances are that someone has already done the work for you.

Start with Google Scholar, e.g. french language vocabulary

A vital search term will be vocabulary or in French vocabulaire

Do a similar thing by searching online for French Language research

You must be prepared to read French, as a lot of research on French will be in French. If you are not fluent in French, you can use automatic translation.

For example

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=vocabulaire+francais&btnG=