For France, the way the rules have been phrased since last summer (so that’s not changing as much as comments imply, even if some new development is always theoretically possible), the distinction has been based on where you are currently coming from / have been in the last 14 days. While non-essential travel is still not advised, there are currently no restrictions based on the purpose of your trip and no need to explain it. This suggests that neither being on a C visa nor coming for a short visit is forbidden.
When France itself was in a lockdown (i.e. French residents movement out of their home was restricted), travel was restricted to some purposes (like business) but residence was not a criteria as such.
Anecdotally, I can tell you that road borders are not policed intensively but the police is still checking train travellers. For non-EU citizens, they do ask for some sort of residence document or visa (together with a passport and proof of PCR test) and I do not know how they would treat a short-stay visa.