I have absolutely no idea how a visa is meant to work within the Schengen zone.
I assume any visa will be an EU one or else it’s impossible to police.
Visas are usually Schengen Visas. They should be issued by the point of entry, so if you enter Schengen via France, you’d usually get a Schengen visa from France. This is pre-Brexit and exactly what that will end up looking like for British citizens post-Brexit is not clear I think. Also, in June there’s a reasonable chance there will still be restrictions on travel between Schengen locations due to COVID, so I’d factor that in to any plans that involve a border. And whilst it will, as others have pointed out, likely to be fairly easy to find crossing points that aren’t staffed like checkpoint charlie was, do expect challenges if your visa was clocked at entry in France and you get stopped 1 month later a long way from there if there are restrictions…